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The rough Hawkes Heston stochastic volatility model Math. Financ. (IF 1.6) Pub Date : 2024-03-02 Alessandro Bondi, Sergio Pulido, Simone Scotti
We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes-type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs
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Naïve Markowitz policies Math. Financ. (IF 1.6) Pub Date : 2024-02-13 Lin Chen, Xun Yu Zhou
We study a continuous-time Markowitz mean–variance portfolio selection model in which a naïve agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naïve policies through the limit of discretely naïve policies that are committed only in very small time intervals, and derive them analytically and explicitly. We compare naïve policies with pre-committed
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Mean-field liquidation games with market drop-out Math. Financ. (IF 1.6) Pub Date : 2024-01-15 Guanxing Fu, Paul P. Hager, Ulrich Horst
We consider a novel class of portfolio liquidation games with market drop-out (“absorption”). More precisely, we consider mean-field and finite player liquidation games where a player drops out of the market when her position hits zero. In particular, round-trips are not admissible. This can be viewed as a no statistical arbitrage condition. In a model with only sellers, we prove that the absorption
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Almost strong equilibria for time-inconsistent stopping problems under finite horizon in continuous time Math. Financ. (IF 1.6) Pub Date : 2023-12-25 Zhou Zhou
We consider time-inconsistent stopping problems for a continuous-time Markov chain under finite time horizon with non-exponential discounting. We provide an example indicating that strong equilibria may not exist in general. As a result, we propose a notion of equilibrium called almost strong equilibrium (ASE), which is a weak equilibrium and satisfies the condition of strong equilibria except at the
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GANs training: A game and stochastic control approach Math. Financ. (IF 1.6) Pub Date : 2023-12-18 Xin Guo, Othmane Mounjid
Training generative adversarial networks (GANs) are known to be difficult, especially for financial time series. This paper first analyzes the well-posedness problem in GANs minimax games and the widely recognized convexity issue in GANs objective functions. It then proposes a stochastic control framework for hyper-parameters tuning in GANs training. The weak form of dynamic programming principle and
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Time-inconsistent contract theory Math. Financ. (IF 1.6) Pub Date : 2023-11-24 Camilo Hernández, Dylan Possamaï
This paper investigates the moral hazard problem in finite horizon with both continuous and lump-sum payments, involving a time-inconsistent sophisticated agent and a standard utility maximizer principal: Building upon the so-called dynamic programming approach in Cvitanić et al. (2018) and the recently available results in Hernández and Possamaï (2023), we present a methodology that covers the previous
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Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations Math. Financ. (IF 1.6) Pub Date : 2023-11-27 Ziheng Wang, Justin Sirignano
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an estimate for the gradient of the stationary distribution. The gradient estimate is simultaneously updated using forward propagation of the SDE state derivatives, asymptotically
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Quantifying dimensional change in stochastic portfolio theory Math. Financ. (IF 1.6) Pub Date : 2023-11-19 Erhan Bayraktar, Donghan Kim, Abhishek Tilva
In this paper, we develop the theory of functional generation of portfolios in an equity market with changing dimension. By introducing dimensional jumps in the market, as well as jumps in stock capitalization between the dimensional jumps, we construct different types of self-financing stock portfolios (additive, multiplicative, and rank-based) in a very general setting. Our study explains how a dimensional
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Sig-Wasserstein GANs for conditional time series generation Math. Financ. (IF 1.6) Pub Date : 2023-11-07 Shujian Liao, Hao Ni, Marc Sabate-Vidales, Lukasz Szpruch, Magnus Wiese, Baoren Xiao
Generative adversarial networks (GANs) have been extremely successful in generating samples, from seemingly high-dimensional probability measures. However, these methods struggle to capture the temporal dependence of joint probability distributions induced by time-series data. Furthermore, long time-series data streams hugely increase the dimension of the target space, which may render generative modeling
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Reference dependence and endogenous anchors Math. Financ. (IF 1.6) Pub Date : 2023-10-25 Paolo Guasoni, Andrea Meireles-Rodrigues
In a complete market, we find optimal portfolios for an investor whose satisfaction stems from both a payoff's intrinsic utility and its comparison with an endogenous reference as modeled by Kőszegi and Rabin. In the regular regime, arising when reference dependence is low, the marginal utility of the optimal payoff is proportional to a twist of the pricing kernel. High reference dependence leads to
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Risk Budgeting portfolios: Existence and computation Math. Financ. (IF 1.6) Pub Date : 2023-10-02 Adil Rengim Cetingoz, Jean-David Fermanian, Olivier Guéant
Modern portfolio theory has provided for decades the main framework for optimizing portfolios. Because of its sensitivity to small changes in input parameters, especially expected returns, the mean–variance framework proposed by Markowitz in 1952 has, however, been challenged by new construction methods that are purely based on risk. Among risk-based methods, the most popular ones are Minimum Variance
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Nonlocality, nonlinearity, and time inconsistency in stochastic differential games Math. Financ. (IF 1.6) Pub Date : 2023-09-21 Qian Lei, Chi Seng Pun
This paper studies the well-posedness of a class of nonlocal fully nonlinear parabolic systems, which nest the equilibrium Hamilton–Jacobi–Bellman (HJB) systems that characterize the time-consistent Nash equilibrium point of a stochastic differential game (SDG) with time-inconsistent (TIC) preferences. The nonlocality of the parabolic systems stems from the flow feature (controlled by an external temporal
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Towards multi-agent reinforcement learning-driven over-the-counter market simulations Math. Financ. (IF 1.6) Pub Date : 2023-09-20 Nelson Vadori, Leo Ardon, Sumitra Ganesh, Thomas Spooner, Selim Amrouni, Jared Vann, Mengda Xu, Zeyu Zheng, Tucker Balch, Manuela Veloso
We study a game between liquidity provider (LP) and liquidity taker agents interacting in an over-the-counter market, for which the typical example is foreign exchange. We show how a suitable design of parameterized families of reward functions coupled with shared policy learning constitutes an efficient solution to this problem. By playing against each other, our deep-reinforcement-learning-driven
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Arbitrage theory in a market of stochastic dimension Math. Financ. (IF 1.6) Pub Date : 2023-09-01 Erhan Bayraktar, Donghan Kim, Abhishek Tilva
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements: (i) there exists a supermartingale numéraire portfolio; (ii) each dissected market, which is of a fixed dimension between dimensional jumps, has locally finite
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Risk concentration and the mean-expected shortfall criterion Math. Financ. (IF 1.6) Pub Date : 2023-08-23 Xia Han, Bin Wang, Ruodu Wang, Qinyu Wu
Expected shortfall (ES, also known as CVaR) is the most important coherent risk measure in finance, insurance, risk management, and engineering. Recently, Wang and Zitikis (2021) put forward four economic axioms for portfolio risk assessment and provide the first economic axiomatic foundation for the family of ES. In particular, the axiom of no reward for concentration (NRC) is arguably quite strong
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Term structure modeling with overnight rates beyond stochastic continuity Math. Financ. (IF 1.6) Pub Date : 2023-08-18 Claudio Fontana, Zorana Grbac, Thorsten Schmidt
Overnight rates, such as the Secured Overnight Financing Rate (SOFR) in the United States, are central to the current reform of interest rate benchmarks. A striking feature of overnight rates is the presence of jumps and spikes occurring at predetermined dates due to monetary policy interventions and liquidity constraints. This corresponds to stochastic discontinuities (i.e., discontinuities occurring
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Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing Math. Financ. (IF 1.6) Pub Date : 2023-08-07 Sebastian Becker, Arnulf Jentzen, Marvin S. Müller, Philippe von Wurstemberger
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of Monte Carlo (MC) simulations. To obtain a good approximation the MC sample size usually needs to be considerably large resulting in a long computing time to obtain
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Robust distortion risk measures Math. Financ. (IF 1.6) Pub Date : 2023-07-29 Carole Bernard, Silvana M. Pesenti, Steven Vanduffel
The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with an absolutely continuous distortion function, its robustness to distributional uncertainty by deriving its largest (smallest) value when the underlying loss distribution
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Insurance–finance arbitrage Math. Financ. (IF 1.6) Pub Date : 2023-07-24 Philippe Artzner, Karl-Theodor Eisele, Thorsten Schmidt
Most insurance contracts are inherently linked to financial markets, be it via interest rates, or—as hybrid products like equity-linked life insurance and variable annuities—directly to stocks or indices. However, insurance contracts are not for trade except sometimes as surrender to the selling office. This excludes the situation of arbitrage by buying and selling insurance contracts at different
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Deep order flow imbalance: Extracting alpha at multiple horizons from the limit order book Math. Financ. (IF 1.6) Pub Date : 2023-07-21 Petter N. Kolm, Jeremy Turiel, Nicholas Westray
We employ deep learning in forecasting high-frequency returns at multiple horizons for 115 stocks traded on Nasdaq using order book information at the most granular level. While raw order book states can be used as input to the forecasting models, we achieve state-of-the-art predictive accuracy by training simpler “off-the-shelf” artificial neural networks on stationary inputs derived from the order
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Mean–variance hedging of contingent claims with random maturity Math. Financ. (IF 1.6) Pub Date : 2023-07-19 Kamil Kladívko, Mihail Zervos
We study the mean–variance hedging of an American-type contingent claim that is exercised at a random time in a Markovian setting. This problem is motivated by applications in the areas of employee stock option valuation, credit risk, or equity-linked life insurance policies with an underlying risky asset value guarantee. Our analysis is based on dynamic programming and uses PDE techniques. In particular
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Crypto quanto and inverse options Math. Financ. (IF 1.6) Pub Date : 2023-07-11 Carol Alexander, Ding Chen, Arben Imeraj
Over 90% of exchange trading on crypto options has always been on the Deribit platform. This centralized crypto exchange only lists inverse products because they do not accept fiat currency. Likewise, other major crypto options platforms only list crypto–stablecoin trading pairs in so-called direct options, which are similar to the standard crypto options listed by the CME except the US dollar is replaced
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Closed-loop Nash competition for liquidity Math. Financ. (IF 1.6) Pub Date : 2023-07-10 Alessandro Micheli, Johannes Muhle-Karbe, Eyal Neuman
We study a multiplayer stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open-loop Nash equilibrium, both the agents' optimal trading rates and their performance
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Predictable forward performance processes: Infrequent evaluation and applications to human-machine interactions Math. Financ. (IF 1.6) Pub Date : 2023-07-02 Gechun Liang, Moris S. Strub, Yuwei Wang
We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a linear functional equation of higher order associated with the inverse problem driving the evolution of the predictable forward process. We provide sufficient conditions
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Clustering heterogeneous financial networks Math. Financ. (IF 1.6) Pub Date : 2023-06-20 Hamed Amini, Yudong Chen, Andreea Minca, Xin Qian
We develop a convex-optimization clustering algorithm for heterogeneous financial networks, in the presence of arbitrary or even adversarial outliers. In the stochastic block model with heterogeneity parameters, we penalize nodes whose degree exhibit unusual behavior beyond inlier heterogeneity. We prove that under mild conditions, this method achieves exact recovery of the underlying clusters. In
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Discrete-time risk sensitive portfolio optimization with proportional transaction costs Math. Financ. (IF 1.6) Pub Date : 2023-06-06 Marcin Pitera, Łukasz Stettner
In this paper we consider a discrete-time risk sensitive portfolio optimization over a long time horizon with proportional transaction costs. We show that within the log-return i.i.d. framework the solution to a suitable Bellman equation exists under minimal assumptions and can be used to characterize the optimal strategies for both risk-averse and risk-seeking cases. Moreover, using numerical examples
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Learning equilibrium mean-variance strategy Math. Financ. (IF 1.6) Pub Date : 2023-06-04 Min Dai, Yuchao Dong, Yanwei Jia
We study a dynamic mean-variance portfolio optimization problem under the reinforcement learning framework, where an entropy regularizer is introduced to induce exploration. Due to the time–inconsistency involved in a mean-variance criterion, we aim to learn an equilibrium policy. Under an incomplete market setting, we obtain a semi-analytical, exploratory, equilibrium mean-variance policy that turns
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Epstein-Zin utility maximization on a random horizon Math. Financ. (IF 1.6) Pub Date : 2023-06-01 Joshua Aurand, Yu-Jui Huang
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded
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Dynamics of market making algorithms in dealer markets: Learning and tacit collusion Math. Financ. (IF 1.6) Pub Date : 2023-05-30 Rama Cont, Wei Xiong
The widespread use of market-making algorithms in electronic over-the-counter markets may give rise to unexpected effects resulting from the autonomous learning dynamics of these algorithms. In particular the possibility of “tacit collusion” among market makers has increasingly received regulatory scrutiny. We model the interaction of market makers in a dealer market as a stochastic differential game
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Trading under the proof-of-stake protocol – A continuous-time control approach Math. Financ. (IF 1.6) Pub Date : 2023-05-24 Wenpin Tang, David D. Yao
We develop a continuous-time control approach to optimal trading in a Proof-of-Stake (PoS) blockchain, formulated as a consumption-investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton–Jacobi–Bellman (HJB) equations. When the utility
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Local volatility under rough volatility Math. Financ. (IF 1.6) Pub Date : 2023-05-24 Florian Bourgey, Stefano De Marco, Peter K. Friz, Paolo Pigato
Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface induced by rough volatility models, supporting their calibration power to SP500 option data. Rough volatility models also generate a local volatility surface, via
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Asymptotic subadditivity/superadditivity of Value-at-Risk under tail dependence Math. Financ. (IF 1.6) Pub Date : 2023-05-15 Wenhao Zhu, Lujun Li, Jingping Yang, Jiehua Xie, Liulei Sun
This paper presents a new method for discussing the asymptotic subadditivity/superadditivity of Value-at-Risk (VaR) for multiple risks. We consider the asymptotic subadditivity and superadditivity properties of VaR for multiple risks whose copula admits a stable tail dependence function (STDF). For the purpose, a marginal region is defined by the marginal distributions of the multiple risks, and a
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A Leland model for delta hedging in central risk books Math. Financ. (IF 1.6) Pub Date : 2023-05-11 Johannes Muhle-Karbe, Zexin Wang, Kevin Webster
Using a tractable extension of the model of Leland (1985), we study how a delta-hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market-making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous-time limit, the optimal limit-order exposure can be computed explicitly by a pointwise maximization
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The log-moment formula for implied volatility Math. Financ. (IF 1.6) Pub Date : 2023-05-11 Vimal Raval, Antoine Jacquier
We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that in the absence of arbitrage, if the underlying stock price at time T admits finite log-moments E [ | log S T | q ] $\mathbb {E}[|\log S_T|^q]$ for some positive q, the arbitrage-free growth in the left wing of the implied volatility smile for T is less constrained than Lee's bound. The result is rationalized
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Equilibrium investment with random risk aversion Math. Financ. (IF 1.6) Pub Date : 2023-05-03 Sascha Desmettre, Mogens Steffensen
We solve the problem of an investor who maximizes utility but faces random preferences. We propose a problem formulation based on expected certainty equivalents. We tackle the time-consistency issues arising from that formulation by applying the equilibrium theory approach. To this end, we provide the proper definitions and prove a rigorous verification theorem. We complete the calculations for the
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Weak equilibria for time-inconsistent control: With applications to investment-withdrawal decisions Math. Financ. (IF 1.6) Pub Date : 2023-04-29 Zongxia Liang, Fengyi Yuan
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the time-inconsistent stopping control problems under general multidimensional controlled diffusion model and propose a formal definition of their equilibria. We show that an admissible pair ( u ̂ , C ) $(\hat{u},C)$
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Designing universal causal deep learning models: The geometric (Hyper)transformer Math. Financ. (IF 1.6) Pub Date : 2023-04-26 Beatrice Acciaio, Anastasis Kratsios, Gudmund Pammer
Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable of encoding these geometric structures remains largely unknown. We address this open problem by introducing a universal causal geometric DL framework in which the
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Reinforcement learning with dynamic convex risk measures Math. Financ. (IF 1.6) Pub Date : 2023-04-17 Anthony Coache, Sebastian Jaimungal
We develop an approach for solving time-consistent risk-sensitive stochastic optimization problems using model-free reinforcement learning (RL). Specifically, we assume agents assess the risk of a sequence of random variables using dynamic convex risk measures. We employ a time-consistent dynamic programming principle to determine the value of a particular policy, and develop policy gradient update
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Trading with the crowd Math. Financ. (IF 1.6) Pub Date : 2023-04-11 Eyal Neuman, Moritz Voß
We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with taking into account a common general price predicting signal. The unique Nash-equilibrium strategies reveal how each agent's liquidation policy adjusts the predictive
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Recent advances in reinforcement learning in finance Math. Financ. (IF 1.6) Pub Date : 2023-04-07 Ben Hambly, Renyuan Xu, Huining Yang
The rapid changes in the finance industry due to the increasing amount of data have revolutionized the techniques on data processing and data analysis and brought new theoretical and computational challenges. In contrast to classical stochastic control theory and other analytical approaches for solving financial decision-making problems that heavily reply on model assumptions, new developments from
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Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps Math. Financ. (IF 1.6) Pub Date : 2023-04-05 Pingping Zeng, Ziqing Xu, Pingping Jiang, Yue Kuen Kwok
We investigate analytical solvability of models with affine stochastic volatility (SV) and Lévy jumps by deriving a unified formula for the conditional moment generating function of the log-asset price and providing the condition under which this new formula is explicit. The results lay a foundation for a range of valuation, calibration, and econometric problems. We then combine our theoretical results
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Credit risk pricing in a consumption-based equilibrium framework with incomplete accounting information Math. Financ. (IF 1.6) Pub Date : 2023-04-03 Junchi Ma, Mobolaji Ogunsolu, Jinniao Qiu, Ayşe Deniz Sezer
We present a consumption-based equilibrium framework for credit risk pricing based on the Epstein–Zin (EZ) preferences where the default time is modeled as the first hitting time of a default boundary and bond investors have imperfect/partial information about the firm value. The imperfect information is generated by the underlying observed state variables and a noisy observation process of the firm
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Equilibria of time-inconsistent stopping for one-dimensional diffusion processes Math. Financ. (IF 1.6) Pub Date : 2023-04-03 Erhan Bayraktar, Zhenhua Wang, Zhou Zhou
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria (introduced in Huang and Nguyen-Huu (2018)), weak equilibria (introduced in Christensen and Lindensjö (2018)), and strong equilibria (introduced in Bayraktar et al. (2021)). The discount function is assumed to be log subadditive and the underlying process is one-dimensional
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Noncausal affine processes with applications to derivative pricing Math. Financ. (IF 1.6) Pub Date : 2023-03-31 Christian Gouriéroux, Yang Lu
Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time. These models are especially relevant for pricing sequences of speculative bubbles. We show that they feature
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Effective algorithms for optimal portfolio deleveraging problem with cross impact Math. Financ. (IF 1.6) Pub Date : 2023-03-30 Hezhi Luo, Yuanyuan Chen, Xianye Zhang, Duan Li, Huixian Wu
We investigate the optimal portfolio deleveraging (OPD) problem with permanent and temporary price impacts, where the objective is to maximize equity while meeting a prescribed debt/equity requirement. We take the real situation with cross impact among different assets into consideration. The resulting problem is, however, a nonconvex quadratic program with a quadratic constraint and a box constraint
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A general approximation method for optimal stopping and random delay Math. Financ. (IF 1.6) Pub Date : 2023-03-20 Pengzhan Chen, Yingda Song
This study examines the continuous-time optimal stopping problem with an infinite horizon under Markov processes. Existing research focuses on finding explicit solutions under certain assumptions of the reward function or underlying process; however, these assumptions may either not be fulfilled or be difficult to validate in practice. We developed a continuous-time Markov chain (CTMC) approximation
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Markov decision processes under model uncertainty Math. Financ. (IF 1.6) Pub Date : 2023-03-17 Ariel Neufeld, Julian Sester, Mario Šikić
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle, we obtain a local-to-global paradigm, namely solving a local, that is, a one time-step robust optimization problem leads to an optimizer of the global (i.e., infinite time-steps) robust stochastic optimal control problem, as
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Preference robust distortion risk measure and its application Math. Financ. (IF 1.6) Pub Date : 2023-02-26 Wei Wang, Huifu Xu
Distortion risk measure (DRM) plays a crucial role in management science and finance particularly actuarial science. Various DRMs have been introduced but little is discussed on which DRM at hand should be chosen to address a decision maker's (DM's) risk preference. This paper aims to fill out the gap. Specifically, we consider a situation where the true distortion function is unknown either because
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Improving reinforcement learning algorithms: Towards optimal learning rate policies Math. Financ. (IF 1.6) Pub Date : 2023-02-26 Othmane Mounjid, Charles-Albert Lehalle
This paper shows how to use results of statistical learning theory and stochastic algorithms to have a better understanding of the convergence of Reinforcement Learning (RL) once it is formulated as a fixed point problem. This can be used to propose improvement of RL learning rates. First, our analysis shows that the classical asymptotic convergence rate O(1/N)$O(1/\sqrt {N})$ is pessimistic and can
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Optimal measure preserving derivatives revisited Math. Financ. (IF 1.6) Pub Date : 2023-02-20 Brendan K. Beare
This article clarifies the relationship between pricing kernel monotonicity and the existence of opportunities for stochastic arbitrage in a complete and frictionless market of derivative securities written on a market portfolio. The relationship depends on whether the payoff distribution of the market portfolio satisfies a technical condition called adequacy, meaning that it is atomless or is comprised
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Reverse stress testing: Scenario design for macroprudential stress tests Math. Financ. (IF 1.6) Pub Date : 2023-02-06 Michel Baes, Eric Schaanning
We propose a systematic algorithmic reverse-stress testing methodology to create “worst case” scenarios for regulatory stress tests by accounting for losses that arise from distressed portfolio liquidations. First, we derive the optimal bank response for any given shock. Then, we introduce an algorithm which systematically generates scenarios that exploit the key vulnerabilities in banks' portfolio
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Model-free portfolio theory: A rough path approach Math. Financ. (IF 1.6) Pub Date : 2023-01-24 Andrew L. Allan, Christa Cuchiero, Chong Liu, David J. Prömel
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on Föllmer integration. Without the assumption of any underlying probabilistic model, we prove a pathwise formula for the relative wealth process, which reduces in the special case
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A model-free approach to continuous-time finance Math. Financ. (IF 1.6) Pub Date : 2023-01-16 Henry Chiu, Rama Cont
We present a pathwise approach to continuous-time finance based on causal functional calculus. Our framework does not rely on any probabilistic concept. We introduce a definition of continuous-time self-financing portfolios, which does not rely on any integration concept and show that the value of a self-financing portfolio belongs to a class of nonanticipative functionals, which are pathwise analogs
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Reconstructing volatility: Pricing of index options under rough volatility Math. Financ. (IF 1.6) Pub Date : 2023-01-13 Peter K. Friz, Thomas Wagenhofer
Avellaneda et al. (2002, 2003) pioneered the pricing and hedging of index options – products highly sensitive to implied volatility and correlation assumptions – with large deviations methods, assuming local volatility dynamics for all components of the index. We present an extension applicable to non-Markovian dynamics and in particular the case of rough volatility dynamics.
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In memoriam: Marco Avellaneda (1955–2022) Math. Financ. (IF 1.6) Pub Date : 2023-01-10 Rama Cont
Marco Avellaneda (1955–2022) was a leading figure in the development of mathematical modeling in finance and its dissemination among market practitioners. We provide a sketch of his trajectory and outline some of his main research contributions to mathematical finance.
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Optimal investment with correlated stochastic volatility factors Math. Financ. (IF 1.6) Pub Date : 2023-01-10 Maxim Bichuch, Jean-Pierre Fouque
The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to a classical distortion transformation. In the present paper, we address the situation with
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Pro-cyclicality beyond business cycle Math. Financ. (IF 1.6) Pub Date : 2022-12-23 Marcel Bräutigam, Michel Dacorogna, Marie Kratz
We show that pro-cyclicality is inherent in risk measure estimates based on historical data. Taking the example of VaR, we show that the empirical VaR measure is mean-reverting over a 1-year horizon when the portfolio is held fixed. It means that a capital requirement rule based on historical measurements of VaR tends in calm times to understate future required capital and tends in volatile times to
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Pathwise CVA regressions with oversimulated defaults Math. Financ. (IF 1.6) Pub Date : 2022-12-23 Lokman A. Abbas-Turki, Stéphane Crépey, Bouazza Saadeddine
We consider the computation by simulation and neural net regression of conditional expectations, or more general elicitable statistics, of functionals of processes (X,Y)$(X,Y)$. Here an exogenous component Y (Markov by itself) is time-consuming to simulate, while the endogenous component X (jointly Markov with Y) is quick to simulate given Y, but is responsible for most of the variance of the simulated
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Algorithmic market making in dealer markets with hedging and market impact Math. Financ. (IF 1.6) Pub Date : 2022-12-05 Alexander Barzykin, Philippe Bergault, Olivier Guéant
In dealer markets, dealers provide prices at which they agree to buy and sell the assets and securities they have in their scope. With ever increasing trading volume, this quoting task has to be done algorithmically in most markets such as foreign exchange (FX) markets or corporate bond markets. Over the last 10 years, many mathematical models have been designed that can be the basis of quoting algorithms