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Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum SIAM J. Financ, Math. (IF 1.0) Pub Date : 2024-03-15 Xun Li, Xiang Yu, Qinyi Zhang
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 121-160, March 2024. Abstract. This paper studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between the nonnegative consumption rate and a fraction of the historical
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Multidimensional Kyle–Back Model with a Risk Averse Informed Trader SIAM J. Financ, Math. (IF 1.0) Pub Date : 2024-03-14 Shreya Bose, Ibrahim Ekren
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 93-120, March 2024. Abstract. We study the continuous time Kyle–Back model with a risk averse informed trader. We show that in a market with multiple assets and non-Gaussian prices an equilibrium exists. The equilibrium is constructed by considering a Fokker–Planck equation and a system of partial differential equations that are coupled
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Short Communication: Optimal Insurance to Maximize Exponential Utility When Premium Is Computed by a Convex Functional SIAM J. Financ, Math. (IF 1.0) Pub Date : 2024-03-08 Jingyi Cao, Dongchen Li, Virginia R. Young, Bin Zou
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page SC15-SC27, March 2024. Abstract. We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the candidate
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Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures SIAM J. Financ, Math. (IF 1.0) Pub Date : 2024-02-27 Jianming Xia
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 54-92, March 2024. Abstract.A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are
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Exploratory Control with Tsallis Entropy for Latent Factor Models SIAM J. Financ, Math. (IF 1.0) Pub Date : 2024-02-05 Ryan Donnelly, Sebastian Jaimungal
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 26-53, March 2024. Abstract. We study optimal control in models with latent factors where the agent controls the distribution over actions, rather than actions themselves, in both discrete and continuous time. To encourage exploration of the state space, we reward exploration with Tsallis entropy and derive the optimal distribution over
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Order Book Queue Hawkes Markovian Modeling SIAM J. Financ, Math. (IF 1.0) Pub Date : 2024-01-30 Philip E. Protter, Qianfan Wu, Shihao Yang
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 1-25, March 2024. Abstract. This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classified intraday order book trading events into a range of categories based on their order types and the price change after their arrivals. In order to capture the stimulating effects
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Short Communication: Are Shortfall Systemic Risk Measures One Dimensional? SIAM J. Financ, Math. (IF 1.0) Pub Date : 2024-01-04 Alessandro Doldi, Marco Frittelli, Emanuela Rosazza Gianin
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page SC1-SC14, March 2024. Abstract. Shortfall systemic (multivariate) risk measures [math] defined through an [math]-dimensional multivariate utility function [math] and random allocations can be represented as classical (1-dimensional) shortfall risk measures associated to an explicitly determined 1-dimensional function constructed from [math]
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Liquidity Based Modeling of Asset Price Bubbles via Random Matching SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-12-15 Francesca Biagini, Andrea Mazzon, Thilo Meyer-Brandis, Katharina Oberpriller
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1304-1342, December 2023. Abstract. In this paper we study the evolution of asset price bubbles driven by contagion effects spreading among investors via a random matching mechanism in a discrete-time version of the liquidity based model of [R. A. Jarrow, P. Protter, and A. F. Roch, Quant. Finance, 12 (2012), pp. 1339–1349]. To this scope
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Short Communication: Existence of Markov Equilibrium Control in Discrete Time SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-12-08 Erhan Bayraktar, Bingyan Han
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page SC60-SC71, December 2023. Abstract. For time-inconsistent stochastic controls in discrete time and finite horizon, an open problem in Björk and Murgoci [Finance Stoch., 18 (2014), pp. 545–592] is the existence of an equilibrium control. A nonrandomized Borel measurable Markov equilibrium policy exists if the objective is inf-compact in
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Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-12-04 Chengfan Gao, Siping Gao, Ruimeng Hu, Zimu Zhu
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1290-1303, December 2023. Abstract. The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [J. Han, A. Jentzen, and W. E, Proc. Natl. Acad. Sci. USA, 115 (2018), pp. 8505–8510] has shown great power in solving high-dimensional
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Short Communication: The Birth of (a Robust) Arbitrage Theory in de Finetti’s Early Contributions SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-11-15 Marco Maggis
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page SC49-SC59, December 2023. Abstract. Il significato soggettivo della probabilità (1931) by B. de Finetti is unanimously considered the rise of “subjectivism,” a notion which strongly influenced both probability and decision theory. What is less acknowledged is that in 1931 de Finetti posed the foundations of modern arbitrage theory. In
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Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-11-14 Anthony Coache, Sebastian Jaimungal, Álvaro Cartea
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1249-1289, December 2023. Abstract.We propose a novel framework to solve risk-sensitive reinforcement learning problems where the agent optimizes time-consistent dynamic spectral risk measures. Based on the notion of conditional elicitability, our methodology constructs (strictly consistent) scoring functions that are used as penalizers
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On Bid and Ask Side-Specific Tick Sizes SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-11-09 Bastien Baldacci, Philippe Bergault, Joffrey Derchu, Mathieu Rosenbaum
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1215-1248, December 2023. Abstract. The tick size, which is the smallest increment between two consecutive prices for a given asset, is a key parameter of market microstructure. In particular, the behavior of high frequency market makers is highly related to its value. We take the point of view of an exchange and investigate the relevance
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Portfolio Optimization within a Wasserstein Ball SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-11-03 Silvana M. Pesenti, Sebastian Jaimungal
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1175-1214, December 2023. Abstract. We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy’s risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lies within a Wasserstein ball surrounding a benchmark’s terminal
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Relative Growth Rate Optimization Under Behavioral Criterion SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-10-25 Jing Peng, Pengyu Wei, Zuo Quan Xu
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1140-1174, December 2023. Abstract. This paper studies a continuous-time optimal portfolio selection problem in a complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor is concerned with the terminal relative growth rate (log-return) instead of absolute capital value
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Pricing Bermudan Options Using Regression Trees/Random Forests SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-10-19 Zineb El Filali Ech-Chafiq, Pierre Henry Labordère, Jérôme Lelong
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1113-1139, December 2023. Abstract. The value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the exercise value is strictly greater than the continuation value. We
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A Mean-Field Game of Market-Making against Strategic Traders SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-10-18 Bastien Baldacci, Philippe Bergault, Dylan Possamaï
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1080-1112, December 2023. Abstract. We design a market-making model à la Avellaneda and Stoikov [Quant. Finance, 8 (2008), pp. 217–224] in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers’
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Short Communication: Is a Sophisticated Agent Always a Wise One? SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-10-17 Jianfeng Zhang
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page SC42-SC48, December 2023. Abstract. For time-inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by sophisticated agents. In this short note, we construct a deterministic continuous-time example where the unique equilibrium is dominated by another control. Therefore, in this situation, it
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Interest Rates Term Structure Models Driven by Hawkes Processes SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-10-17 Guillaume Bernis, Matthieu Garcin, Simone Scotti, Carlo Sgarra
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1062-1079, December 2023. Abstract. This paper includes a marked Hawkes process in the original Heath–Jarrow–Morton (HJM) setup and investigates the impact of this assumption on the pricing of the popular vanilla fixed-income derivatives. Our model exhibits a smile that can fit the implied volatility of swaptions for a given key rate (tenor)
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A Neural Network Approach to High-Dimensional Optimal Switching Problems with Jumps in Energy Markets SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-10-16 Erhan Bayraktar, Asaf Cohen, April Nellis
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1028-1061, December 2023. Abstract. We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then apply this algorithm to a variety of energy scheduling problems
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Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-10-11 Brian (Xin) Ning, Sebastian Jaimungal, Xiaorong Zhang, Maxime Bergeron
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1004-1027, December 2023. Abstract. We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free variational autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven models. We focus on two classes of SDE models: regime switching
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Cubature Method for Stochastic Volterra Integral Equations SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-10-10 Qi Feng, Jianfeng Zhang
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 959-1003, December 2023. Abstract. In this paper, we introduce the cubature formula for stochastic Volterra integral equations. We first derive the stochastic Taylor expansion in this setting, by utilizing a functional Itô formula, and provide its tail estimates. We then introduce the cubature measure for such equations, and construct
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Short Communication: Exponential Utility Maximization in a Discrete Time Gaussian Framework SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-09-05 Yan Dolinsky, Or Zuk
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page SC31-SC41, September 2023. Abstract. The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in mathematical finance, we also consider an investor who is informed
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Signature-Based Models: Theory and Calibration SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-08-17 Christa Cuchiero, Guido Gazzani, Sara Svaluto-Ferro
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 910-957, September 2023. Abstract. We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional continuous semimartingale. The framework is universal in the sense that
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How Rough Path Lifts Affect Expected Return and Volatility: A Rough Model under Transaction Cost SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-08-10 Luu H. Duc, Jürgen Jost
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 879-909, September 2023. Abstract. We develop a general mathematical framework, based on rough path theory that can incorporate the empirically observed nonlinear mean-variance relation of the logarithmic return in a systematic manner. This model offers the possibility of an additional noise hidden in the rough path lift, hence supporting
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Optimal Brokerage Contracts in Almgren–Chriss Model with Multiple Clients SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-08-08 Guillermo Alonso Alvarez, Sergey Nadtochiy, Kevin Webster
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 855-878, September 2023. Abstract. This paper constructs optimal brokerage contracts for multiple (heterogeneous) clients trading a single asset whose price follows the Almgren–Chriss model. The distinctive features of this work are as follows: (i) the reservation values of the clients are determined endogenously, and (ii) the broker is
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Constrained Monotone Mean-Variance Problem with Random Coefficients SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-08-01 Ying Hu, Xiaomin Shi, Zuo Quan Xu
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 838-854, September 2023. Abstract. This paper studies the monotone mean-variance problem and the classical mean-variance problem with convex cone trading constraints in a market with random coefficients. We provide semiclosed optimal strategies and optimal values for both problems via certain backward stochastic differential equations
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Capital Growth and Survival Strategies in a Market with Endogenous Prices SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-08-01 Mikhail Zhitlukhin
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 812-837, September 2023. Abstract. We consider a multiagent asset market model which includes assets of two types: long-lived assets with exogenous prices and short-lived assets with endogenous prices. The first main result consists of constructing a strategy which allows an agent to maintain a nonvanishing share of market wealth over
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Optimal Execution with Quadratic Variation Inventories SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-07-13 Rene Carmona, Laura Leal
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 751-776, September 2023. Abstract. The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intraday data from the Toronto Stock Exchange to provide empirical evidence of this claim
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Optimal Stopping for Exponential Lévy Models with Weighted Discounting SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-07-13 David Landriault, Bin Li, José M. Pedraza
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 777-811, September 2023. Abstract. This paper considers an optimal stopping problem with weighted discounting, and the state process is modeled by a general exponential Lévy process. Due to the time inconsistency, we provide a new martingale method based on a verification theorem for the equilibrium stopping strategies. As an application
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Robust Control Problems of BSDEs Coupled with Value Functions SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-07-10 Zhou Yang, Jing Zhang, Chao Zhou
SIAM Journal on Financial Mathematics, Volume 14, Issue 3, Page 721-750, September 2023. Abstract. The paper considers a robust control problem, where the controlled stochastic differential equations (SDEs) include ambiguity parameters and have coefficients satisfying non-Lipschitz continuous and nonlinear growth conditions, and the objective function is expressed as a backward stochastic differential
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Sensitivity of Multiperiod Optimization Problems with Respect to the Adapted Wasserstein Distance SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-06-12 Daniel Bartl, Johannes Wiesel
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 704-720, June 2023. Abstract. We analyze the effect of small changes in the underlying probabilistic model on the value of multiperiod stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the adapted Wasserstein distance. We prove explicit first-order approximations
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Robustness of Delta Hedging in a Jump-Diffusion Model SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-06-05 Frank Bosserhoff, Mitja Stadje
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 663-703, June 2023. Abstract. Suppose an investor aims at Delta hedging a European contingent claim [math] in a jump-diffusion model, but incorrectly specifies the stock price’s volatility and jump sensitivity, so that any hedging strategy is calculated under a misspecified model. When does the erroneously computed strategy approximate
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One Axiom to Rule Them All: A Minimalist Axiomatization of Quantiles SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-06-01 Tolulope Fadina, Peng Liu, Ruodu Wang
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 644-662, June 2023. Abstract. We offer a minimalist axiomatization of quantiles among all real-valued mappings on a general set of distributions through only one axiom. This axiom is called ordinality: Quantiles are the only mappings that commute with all increasing and continuous transforms. Other convenient properties of quantiles—monotonicity
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Analysis of Bank Leverage via Dynamical Systems and Deep Neural Networks SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-05-31 Fabrizio Lillo, Giulia Livieri, Stefano Marmi, Anton Solomko, Sandro Vaienti
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 598-643, June 2023. Abstract. We consider a model of a simple financial system consisting of a leveraged investor that invests in a risky asset and manages risk by using value-at-risk (VaR). The VaR is estimated by using past data via an adaptive expectation scheme. We show that the leverage dynamics can be described by a dynamical system
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Optimal Consumption Under a Habit-Formation Constraint: The Deterministic Case SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-05-26 Bahman Angoshtari, Erhan Bayraktar, Virginia R. Young
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 557-597, June 2023. Abstract. We formulate and solve a deterministic optimal consumption problem to maximize the discounted constant relative risk aversion utility of an individual’s consumption-to-habit process assuming they only invest in a riskless market and that they are unwilling to consume at a rate below a certain proportion [math]
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Geometric Characterization of Maximum Diversification Return Portfolio via Rao’s Quadratic Entropy SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-05-24 Hou-Duo Qi
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 525-556, June 2023. Abstract. Diversification return has been well studied in finance literature, mainly focusing on the various sources from which it may be generated. The maximization of diversification return, in its natural form, is often handed over to convex quadratic optimization for its solution. In this paper, we study the maximization
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Optimal Dividends Under Model Uncertainty SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-05-17 Prakash Chakraborty, Asaf Cohen, Virginia R. Young
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 497-524, June 2023. Abstract. We consider a diffusive model for optimally distributing dividends, while allowing for Knightian model ambiguity concerning the drift of the surplus process. We show that the value function is the unique solution of a nonlinear Hamilton–Jacobi–Bellman variational inequality. In addition, this value function
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Weak Error Rates of Numerical Schemes for Rough Volatility SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-05-17 Paul Gassiat
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 475-496, June 2023. Abstract. Simulation of rough volatility models involves discretization of stochastic integrals where the integrand is a function of a (correlated) fractional Brownian motion (fBm) of Hurst index [math]. We obtain results on the rate of convergence in the number of time-steps for the weak error of such approximations
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Extensions of Dupire Formula: Stochastic Interest Rates and Stochastic Local Volatility SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-05-12 Orcan Ögetbil, Bernhard Hientzsch
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 452-474, June 2023. Abstract. We derive generalizations of the Dupire formula to the case of general stochastic drift and/or the case of general stochastic local volatility. First, we handle the case in which the drift is given as a difference of two stochastic short rates. Such a setting is natural in a foreign exchange context where
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Beating a Benchmark: Dynamic Programming May Not Be the Right Numerical Approach SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-05-10 Pieter M. Van Staden, Peter A. Forsyth, Yuying Li
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 407-451, June 2023. Abstract. We analyze dynamic investment strategies for benchmark outperformance using two widely used objectives of practical interest to investors: (i) maximizing the information ratio (IR), and (ii) obtaining a favorable tracking difference (cumulative outperformance) relative to the benchmark. In the case of the
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Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-04-25 Christian Bayer, Martin Eigel, Leon Sallandt, Philipp Trunschke
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 383-406, June 2023. Abstract. An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the “curse of dimensionality” can be alleviated for the computation of Bermudan option prices with the Monte Carlo least-squares approach as well as the dual martingale method
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Deep Curve-Dependent PDEs for Affine Rough Volatility SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-04-25 Antoine Jacquier, Mugad Oumgari
SIAM Journal on Financial Mathematics, Volume 14, Issue 2, Page 353-382, June 2023. Abstract. We introduce a new deep learning–based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE, depending on forward curves rather than the whole path of the process, we develop a numerical scheme based on deep learning
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Short Communication: A Primer on Perpetuals SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-03-30 Guillermo Angeris, Tarun Chitra, Alex Evans, Matthew Lorig
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page SC17-SC30, March 2023. Abstract. We consider a continuous-time financial market with no arbitrage and no transactions costs. In this setting, we introduce two types of perpetual contracts, one in which the payoff to the long side is a fixed function of the underlyers and the long side pays a funding rate to the short side, the other in
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Deep xVA Solver: A Neural Network–Based Counterparty Credit Risk Management Framework SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-03-30 Alessandro Gnoatto, Athena Picarelli, Christoph Reisinger
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 314-352, March 2023. Abstract. In this paper, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method utilizes a coupled system of BSDEs for the valuation adjustments (xVA)
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Short Communication: Caplet Pricing in Affine Models for Alternative Risk-Free Rates SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-03-10 Claudio Fontana
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page SC1-SC16, March 2023. Abstract. Alternative risk-free rates (RFRs) play a central role in the reform of interest rate benchmarks. We study a short-rate model for RFRs driven by a general affine process. In this context, under minimal assumptions, we derive explicit valuation formulas for forward-looking and backward-looking caplets/floorlets
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Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-03-03 Pablo Azcue, Xiaoqing Liang, Nora Muler, Virginia R. Young
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 279-313, March 2023. Abstract. In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cramér–Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We extend the work of Liang, Liang, and Young [Insurance Math. Econom., 92
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Pricing Principle via Tsallis Relative Entropy in Incomplete Markets SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-02-07 Dejian Tian
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 250-278, March 2023. Abstract. A pricing principle is introduced for nonattainable [math]-exponential bounded contingent claims in an incomplete Brownian motion market setting. The buyer evaluates the contingent claim under the “distorted Radon–Nikodym derivative” and adjustment by Tsallis relative entropy over a family of equivalent martingale
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On the Discrete-Time Simulation of the Rough Heston Model SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-02-07 Alexandre Richard, Xiaolu Tan, Fan Yang
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 223-249, March 2023. Abstract. We study Euler-type discrete-time schemes for the rough Heston model, which can be described by a stochastic Volterra equation (with non-Lipschitz coefficient functions) or by an equivalent integrated variance formulation. Using weak convergence techniques, we prove that the limits of the discrete-time schemes
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A Random-Supply Mean Field Game Price Model SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-02-07 Diogo Gomes, Julian Gutierrez, Ricardo Ribeiro
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 188-222, March 2023. Abstract. We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading costs, the market clears, and supply meets demand. This problem arises
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Contingent Convertible Obligations and Financial Stability SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-01-27 Zachary Feinstein, Thomas R. Hurd
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 158-187, March 2023. Abstract. This paper investigates whether a financial system can be made more stable if financial institutions share risk by exchanging contingent convertible (CoCo) debt obligations. The question is framed in a financial network model of debt and equity interlinkages with the addition of a variant of the CoCo that
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Bayesian Estimation and Optimization for Learning Sequential Regularized Portfolios SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-01-27 Godeliva Petrina Marisu, Chi Seng Pun
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 127-157, March 2023. Abstract. This paper incorporates Bayesian estimation and optimization into a portfolio selection framework, particularly for high-dimensional portfolios in which the number of assets is larger than the number of observations. We leverage a constrained [math] minimization approach, called the linear programming optimal
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Normal Tempered Stable Processes and the Pricing of Energy Derivatives SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-01-24 Piergiacomo Sabino
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 99-126, March 2023. Abstract. In this study we consider the pricing of energy derivatives when the evolution of spot prices is modeled with a normal tempered stable driven Ornstein–Uhlenbeck process. Such processes are the generalization of normal inverse Gaussian processes that are widely used in energy finance applications. We first
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Utility Maximization in Multivariate Volterra Models SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-01-19 Florian Aichinger, Sascha Desmettre
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 52-98, March 2023. Abstract. This paper is concerned with portfolio selection for an investor with power utility in multiasset financial markets in a rough stochastic environment. We investigate Merton’s portfolio problem for different multivariate Volterra models, covering the rough Heston model. First we consider a class of multivariate
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Jump Diffusion Approximation for the Price Dynamics of a Fully State Dependent Limit Order Book Model SIAM J. Financ, Math. (IF 1.0) Pub Date : 2023-01-19 Dörte Kreher, Cassandra Milbradt
SIAM Journal on Financial Mathematics, Volume 14, Issue 1, Page 1-51, March 2023. Abstract. We study a microscopic limit order book model, in which the order dynamics depend on the current best bid and ask price and the current volume density functions, simultaneously, and derive its macroscopic high-frequency dynamics. As opposed to the existing literature on scaling limits for limit order book models
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The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew SIAM J. Financ, Math. (IF 1.0) Pub Date : 2022-12-08 Julien Guyon
SIAM Journal on Financial Mathematics, Volume 13, Issue 4, Page 1418-1485, December 2022. Using the exponential generating function of Hermite polynomials, we expand the prices of VIX power payoffs (including VIX futures) in various Bergomi models at any order in the volatility-of-volatility. We introduce the notion of volatility of the VIX squared implied by a VIX power payoff, which we call “implied
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Double-Execution Strategies Using Path Signatures SIAM J. Financ, Math. (IF 1.0) Pub Date : 2022-11-21 Álvaro Cartea, Imanol Pérez Arribas, Leandro Sánchez-Betancourt
SIAM Journal on Financial Mathematics, Volume 13, Issue 4, Page 1379-1417, December 2022. We employ the expected signature of equity and foreign exchange markets to derive an optimal double-execution trading strategy. The signature of a path of a stochastic process is a sequence of real numbers that provides a full description of the evolution of the process. The double-execution strategy maximizes
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Separability Versus Robustness of Orlicz Spaces: Financial and Economic Perspectives SIAM J. Financ, Math. (IF 1.0) Pub Date : 2022-11-21 Felix-Benedikt Liebrich, Max Nendel
SIAM Journal on Financial Mathematics, Volume 13, Issue 4, Page 1344-1378, December 2022. We investigate robust Orlicz spaces as a generalization of robust $L^p$-spaces. Two constructions of such spaces are distinguished, a top-down approach and a bottom-up approach. We show that separability of robust Orlicz spaces or their subspaces has very strong implications in terms of the dominatedness of the
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Short Communication: Stability of Time-Inconsistent Stopping for One-Dimensional Diffusions SIAM J. Financ, Math. (IF 1.0) Pub Date : 2022-11-18 Erhan Bayraktar, Zhenhua Wang, Zhou Zhou
SIAM Journal on Financial Mathematics, Volume 13, Issue 4, Page SC123-SC135, December 2022. Abstract. We investigate the stability of the equilibrium-induced optimal value in a one-dimensional diffusion setting for a time-inconsistent stopping problem under nonexponential discounting. We show that the optimal value is semicontinuous with respect to the drift, volatility, and reward function. An example
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Endogenous Noise Trackers in a Radner Equilibrium SIAM J. Financ, Math. (IF 1.0) Pub Date : 2022-10-26 Jin Hyuk Choi, Kim Weston
SIAM Journal on Financial Mathematics, Volume 13, Issue 4, Page 1326-1343, December 2022. We prove the existence of an incomplete Radner equilibrium in a model with exponential investors and an endogenous noise tracker. We analyze a coupled system of ODEs and reduce it to a system of two coupled ODEs in order to establish equilibrium existence. As an application, we study the impact of the endogenous