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  • On utility maximization under model uncertainty in discrete‐time markets
    Math. Financ. (IF 2.25) Pub Date : 2020-07-23
    Miklós Rásonyi; Andrea Meireles‐Rodrigues

    We study the problem of maximizing terminal utility for an agent facing model uncertainty, in a frictionless discrete‐time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either on the positive real line or on the whole real line, is bounded from above. We further find that the boundedness assumption can

    更新日期:2020-07-23
  • Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case
    Math. Financ. (IF 2.25) Pub Date : 2020-07-20
    Erhan Bayraktar; Thomas Cayé; Ibrahim Ekren

    We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small nonlinear price impact. In our model, cross‐impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around its frictionless version. The leading order correction is characterized by a nonlinear

    更新日期:2020-07-20
  • Continuous‐time mean–variance portfolio selection: A reinforcement learning framework
    Math. Financ. (IF 2.25) Pub Date : 2020-06-23
    Haoran Wang; Xun Yu Zhou

    We approach the continuous‐time mean–variance portfolio selection with reinforcement learning (RL). The problem is to achieve the best trade‐off between exploration and exploitation, and is formulated as an entropy‐regularized, relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian, with time‐decaying variance. We then prove a policy improvement

    更新日期:2020-06-24
  • Optimal investment, derivative demand, and arbitrage under price impact
    Math. Financ. (IF 2.25) Pub Date : 2020-06-22
    Michail Anthropelos; Scott Robertson; Konstantinos Spiliopoulos

    This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear

    更新日期:2020-06-23
  • A term structure model for dividends and interest rates
    Math. Financ. (IF 2.25) Pub Date : 2020-06-16
    Damir Filipović; Sander Willems

    Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump‐diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. We present an efficient moment based approximation method

    更新日期:2020-06-16
  • Convergence of optimal expected utility for a sequence of discrete‐time markets
    Math. Financ. (IF 2.25) Pub Date : 2020-06-16
    David M. Kreps; Walter Schachermayer

    We examine Kreps' conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete‐time economies that “approach” the BSM economy in a natural sense: The n th discrete‐time economy is generated by a scaled n ‐step random walk, based on an unscaled random variable ζ with mean 0, variance 1, and bounded support

    更新日期:2020-06-16
  • Robust risk aggregation with neural networks
    Math. Financ. (IF 2.25) Pub Date : 2020-06-13
    Stephan Eckstein; Michael Kupper; Mathias Pohl

    We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure

    更新日期:2020-06-13
  • When to sell an asset amid anxiety about drawdowns
    Math. Financ. (IF 2.25) Pub Date : 2020-06-12
    Neofytos Rodosthenous; Hongzhong Zhang

    We consider risk‐averse investors with different levels of anxiety about asset price drawdowns. The latter is defined as the distance of the current price away from its best performance since inception. These drawdowns can increase either continuously or by jumps, and will contribute toward the investor's overall impatience when breaching the investor's private tolerance level. We investigate the unusual

    更新日期:2020-06-12
  • Network valuation in financial systems
    Math. Financ. (IF 2.25) Pub Date : 2020-06-01
    Paolo Barucca; Marco Bardoscia; Fabio Caccioli; Marco D'Errico; Gabriele Visentin; Guido Caldarelli; Stefano Battiston

    We introduce a general model for the balance‐sheet consistent valuation of interbank claims within an interconnected financial system. Our model represents an extension of clearing models of interdependent liabilities to account for the presence of uncertainty on banks' external assets. At the same time, it also provides a natural extension of classic structural credit risk models to the case of an

    更新日期:2020-06-01
  • Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm
    Math. Financ. (IF 2.25) Pub Date : 2020-05-27
    Denis Belomestny; Maxim Kaledin; John Schoenmakers

    In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete‐ and continuous‐time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete‐time case the WSM algorithm

    更新日期:2020-05-27
  • Risk functionals with convex level sets
    Math. Financ. (IF 2.25) Pub Date : 2020-05-27
    Ruodu Wang; Yunran Wei

    We analyze the “convex level sets” (CxLS) property of risk functionals, which is a necessary condition for the notions of elicitability, identifiability, and backtestability, popular in the recent statistics and risk management literature. We put the CxLS property in the multidimensional setting, with a special focus on signed Choquet integrals, a class of risk functionals that are generally not monotone

    更新日期:2020-05-27
  • Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds
    Math. Financ. (IF 2.25) Pub Date : 2020-05-21
    Angelos Dassios; Jia Wei Lim; Yan Qu

    In this paper, we study the excursions of Bessel and Cox–Ingersoll–Ross (CIR) processes with dimensions . We obtain densities for the last passage times and meanders of the processes. Using these results, we prove a variation of the Azéma martingale for the Bessel and CIR processes based on excursion theory. Furthermore, we study their Parisian excursions, and generalize previous results on the Parisian

    更新日期:2020-05-21
  • Self‐similarity in long‐horizon returns
    Math. Financ. (IF 2.25) Pub Date : 2020-05-05
    Dilip B. Madan; Wim Schoutens

    Asset returns incorporate new information via the effects of independent and possibly identically distributed random shocks. They may also incorporate long memory effects related to the concept of self‐similarity. The two approaches are here combined. In addition, methods are proposed for estimating the contribution of each component and evidence supporting the presence of both components in both the

    更新日期:2020-05-05
  • Cover Image, Volume 30, Issue 2
    Math. Financ. (IF 2.25) Pub Date : 2020-03-19

    The cover image is based on the Original Article Semistatic and Sparse Variance‐Optimal Hedging by Di Tella et al., https://doi.org/10.1111/mafi.12235.

    更新日期:2020-04-22
  • Asset pricing with heterogeneous beliefs and illiquidity
    Math. Financ. (IF 2.25) Pub Date : 2020-04-16
    Johannes Muhle‐Karbe; Marcel Nutz; Xiaowei Tan

    This paper studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset's payoff. We propose a tractable model where agents maximize expected returns under quadratic costs on inventories and trading rates. The unique equilibrium price is characterized by a weakly coupled system of linear parabolic

    更新日期:2020-04-22
  • No‐arbitrage implies power‐law market impact and rough volatility
    Math. Financ. (IF 2.25) Pub Date : 2020-03-24
    Paul Jusselin; Mathieu Rosenbaum

    Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that in a quite general framework, under no‐arbitrage assumption, the market impact function can only be of power‐law type. Furthermore, we prove this implies that the macroscopic price is diffusive with rough volatility, with a one‐to‐one correspondence between the

    更新日期:2020-04-22
  • Effective risk aversion in thin risk‐sharing markets
    Math. Financ. (IF 2.25) Pub Date : 2020-04-12
    Michail Anthropelos; Constantinos Kardaras; Georgios Vichos

    We consider thin incomplete financial markets, where traders with heterogeneous preferences and risk exposures have motive to behave strategically regarding the demand schedules they submit, thereby impacting prices and allocations. We argue that traders relatively more exposed to the market portfolio tend to behave in a more risk tolerant manner. Noncompetitive equilibrium prices and allocations result

    更新日期:2020-04-12
  • Distress and default contagion in financial networks
    Math. Financ. (IF 2.25) Pub Date : 2020-04-12
    Luitgard Anna Maria Veraart

    We develop a new model for solvency contagion that can be used to quantify systemic risk in stress tests of financial networks. In contrast to many existing models, it allows for the spread of contagion already before the point of default and hence can account for contagion due to distress and mark‐to‐market losses. We derive general ordering results for outcome measures of stress tests that enable

    更新日期:2020-04-12
  • Lifetime investment and consumption with recursive preferences and small transaction costs
    Math. Financ. (IF 2.25) Pub Date : 2020-04-08
    Yaroslav Melnyk; Johannes Muhle‐Karbe; Frank Thomas Seifried

    We investigate the effects of small proportional transaction costs on lifetime consumption and portfolio choice. The extant literature has focused on agents with additive utilities. Here, we extend this analysis to the archetype of nonadditive preferences: the isoelastic recursive utilities proposed by Epstein and Zin.

    更新日期:2020-04-08
  • A martingale representation theorem and valuation of defaultable securities
    Math. Financ. (IF 2.25) Pub Date : 2020-04-08
    Tahir Choulli; Catherine Daveloose; Michèle Vanmaele

    We consider a financial framework with two levels of information: the public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can represent many economic and financial settings, such as the default time of a firm for credit risk, and the death time of an insured for life insurance. As the random

    更新日期:2020-04-08
  • Optimal equilibria for time‐inconsistent stopping problems in continuous time
    Math. Financ. (IF 2.25) Pub Date : 2020-03-04
    Yu‐Jui Huang; Zhou Zhou

    For an infinite‐horizon continuous‐time optimal stopping problem under nonexponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log sub‐additive and the state process is one‐dimensional, an optimal equilibrium is constructed in a specific form, under appropriate regularity and

    更新日期:2020-03-20
  • Robust XVA
    Math. Financ. (IF 2.25) Pub Date : 2020-03-12
    Maxim Bichuch; Agostino Capponi; Stephan Sturm

    We introduce an arbitrage‐free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the exact return rate of her counterparty's bond, but she knows it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process

    更新日期:2020-03-12
  • Hedging nontradable risks with transaction costs and price impact
    Math. Financ. (IF 2.25) Pub Date : 2020-03-12
    Álvaro Cartea; Ryan Donnelly; Sebastian Jaimungal

    A risk‐averse agent hedges her exposure to a nontradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross‐impact. By solving the agent's stochastic control problem, we obtain a closed‐form expression for the optimal strategy when the agent holds a linear position in U . When the exposure

    更新日期:2020-03-12
  • Static and semistatic hedging as contrarian or conformist bets
    Math. Financ. (IF 2.25) Pub Date : 2020-03-12
    Svetlana Boyarchenko; Sergei Levendorskiĭ

    In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semistatic portfolios should more properly be thought of as separate classes of derivatives, with nontrivial, model‐dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from the Carr–Madan

    更新日期:2020-03-12
  • Shortfall aversion
    Math. Financ. (IF 2.25) Pub Date : 2020-03-04
    Paolo Guasoni; Gur Huberman; Dan Ren

    Shortfall aversion reflects the higher utility loss of spending cuts from a reference than the utility gain from similar spending increases. Inspired by Prospect Theory's loss aversion and the peak‐end rule, this paper posits a model of utility from spending scaled by past peak spending. In contrast to traditional models, which call for spending rates proportional to wealth, the optimal policy in this

    更新日期:2020-03-04
  • Dividend policy and capital structure of a defaultable firm
    Math. Financ. (IF 2.25) Pub Date : 2020-03-04
    Alex S. L. Tse

    Default risk significantly affects the corporate policies of a firm. We develop a model in which a limited liability entity subject to default at an exponential random time jointly sets its dividend policy and capital structure to maximize the expected lifetime utility from consumption of risk‐averse equity investors. We give a complete characterization of the solution to the singular stochastic control

    更新日期:2020-03-04
  • Semimartingale theory of monotone mean–variance portfolio allocation
    Math. Financ. (IF 2.25) Pub Date : 2020-03-04
    Aleš Černý

    We study dynamic optimal portfolio allocation for monotone mean–variance preferences in a general semimartingale model. Armed with new results in this area, we revisit the work of Cui et al. and fully characterize the circumstances under which one can set aside a nonnegative cash flow while simultaneously improving the mean–variance efficiency of the left‐over wealth. The paper analyzes, for the first

    更新日期:2020-03-04
  • Mean‐field games with differing beliefs for algorithmic trading
    Math. Financ. (IF 2.25) Pub Date : 2020-02-25
    Philippe Casgrain; Sebastian Jaimungal

    Even when confronted with the same data, agents often disagree on a model of the real world. Here, we address the question of how interacting heterogeneous agents, who disagree on what model the real world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for the permanent impact they have on prices. This leads to a large stochastic game, where

    更新日期:2020-02-25
  • A regularity structure for rough volatility
    Math. Financ. (IF 2.25) Pub Date : 2019-11-19
    Christian Bayer; Peter K. Friz; Paul Gassiat; Jorg Martin; Benjamin Stemper

    A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility. First observed by Gatheral et al. in high‐frequency data, subsequently derived within market microstructure models, rough volatility captures parsimoniously key‐stylized facts of the entire implied volatility surface, including extreme skews (as observed earlier by Alòs et al.) that were thought to be outside

    更新日期:2019-11-19
  • Existence of a calibrated regime switching local volatility model
    Math. Financ. (IF 2.25) Pub Date : 2019-11-18
    Benjamin Jourdain; Alexandre Zhou

    By Gyöngy's theorem, a local and stochastic volatility model is calibrated to the market prices of all European call options with positive maturities and strikes if its local volatility (LV) function is equal to the ratio of the Dupire LV function over the root conditional mean square of the stochastic volatility factor given the spot value. This leads to a stochastic differential equation (SDE) nonlinear

    更新日期:2019-11-18
  • Dynamically consistent alpha‐maxmin expected utility
    Math. Financ. (IF 2.25) Pub Date : 2019-11-17
    Patrick Beissner; Qian Lin; Frank Riedel

    The alpha‐maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of alpha. In this paper, we derive a recursive, dynamically consistent version of the alpha‐maxmin model. In the continuous‐time limit, the resulting dynamic utility function can

    更新日期:2019-11-17
  • Nonlinear price impact and portfolio choice
    Math. Financ. (IF 2.25) Pub Date : 2019-11-11
    Paolo Guasoni; Marko Hans Weber

    In a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long‐term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the

    更新日期:2019-11-11
  • Consistency of option prices under bid-ask spreads.
    Math. Financ. (IF 2.25) Pub Date : 2019-11-11
    Stefan Gerhold,Ismail Cetin Gülüm

    Given a finite set of European call option prices on a single underlying, we want to know when there is a market model that is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a bid-ask spread. The main question then is how large (in terms of a deterministic bound) this spread must be to explain the given prices. We fully solve this problem

    更新日期:2019-11-11
  • Semistatic and sparse variance‐optimal hedging
    Math. Financ. (IF 2.25) Pub Date : 2019-11-11
    Paolo Di Tella; Martin Haubold; Martin Keller‐Ressel

    We consider the problem of hedging a contingent claim with a “semistatic” strategy composed of a dynamic position in one asset and static (buy‐and‐hold) positions in other assets. We give general representations of the optimal strategy and the hedging error under the criterion of variance optimality and provide tractable formulas using Fourier integration in case of the Heston model. We also consider

    更新日期:2019-11-11
  • Optimal equilibria for time‐inconsistent stopping problems in continuous time
    Math. Financ. (IF 2.25) Pub Date : 2019-11-07
    Yu‐Jui Huang; Zhou Zhou

    For an infinite‐horizon continuous‐time optimal stopping problem under nonexponential discounting, we look for an optimal equilibrium , which generates larger values than any other equilibrium does on the entire state space. When the discount function is log subadditive and the state process is one‐dimensional, an optimal equilibrium is constructed in a specific form, under appropriate regularity and

    更新日期:2019-11-07
  • Pathwise moderate deviations for option pricing
    Math. Financ. (IF 2.25) Pub Date : 2019-11-07
    Antoine Jacquier; Konstantinos Spiliopoulos

    We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling enables us to transfer these results into small‐time, large‐time, and tail asymptotics for diffusions, as well as for option prices and realized variances. In passing, we highlight some intuitive relationships between moderate deviations

    更新日期:2019-11-07
  • Pricing collateralized derivatives with an arbitrary numeraire
    Math. Financ. (IF 2.25) Pub Date : 2019-11-06
    Joanne Kennedy

    Since the 2008 crisis collateralized derivatives have become commonplace in the market. There have been many papers in recent years on pricing collateralized derivatives but the topic has been surrounded by confusion with debate focusing on whether or not a risk‐free rate needs to be assumed. In addition, as pointed out by Bielecki and Rutkowski, several authors do not pay enough attention to the pricing

    更新日期:2019-11-06
  • Firm capital dynamics in centrally cleared markets
    Math. Financ. (IF 2.25) Pub Date : 2019-11-06
    Agostino Capponi; W. Allen Cheng; Sriram Rajan

    We develop a tractable continuous time model of multifirm capital dynamics in a centrally cleared market. Our framework jointly models the strategic interactions between business operations of firms and their trading activities. We show that the endogenous allocation of firm capital between trading and operations can be recovered as the unique fixed point of a system of quadratic equations. Our model

    更新日期:2019-11-06
  • Option pricing in the moderate deviations regime.
    Math. Financ. (IF 2.25) Pub Date : 2018-07-19
    Peter Friz,Stefan Gerhold,Arpad Pinter

    We consider call option prices close to expiry in diffusion models, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money and out-of-the-money regimes. First and higher order small-time moderate deviation estimates of call prices and implied volatilities are obtained. The expansions involve only simple expressions of the model parameters

    更新日期:2019-11-01
  • Cover's universal portfolio, stochastic portfolio theory, and the numéraire portfolio.
    Math. Financ. (IF 2.25) Pub Date : null
    Christa Cuchiero,Walter Schachermayer,Ting-Kam Leonard Wong

    Cover's celebrated theorem states that the long-run yield of a properly chosen "universal" portfolio is almost as good as that of the best retrospectively chosen constant rebalanced portfolio. The "universality" refers to the fact that this result is model-free, that is, not dependent on an underlying stochastic process. We extend Cover's theorem to the setting of stochastic portfolio theory: the market

    更新日期:2019-11-01
  • Optimal consumption and investment with liquid and illiquid assets
    Math. Financ. (IF 2.25) Pub Date : 2019-07-15
    Jin Hyuk Choi

    I consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio that consists of one bond, one liquid risky asset (no transaction costs), and one illiquid risky asset (proportional transaction costs). I fully characterize the optimal consumption and trading strategies in terms of the solution of

    更新日期:2019-07-15
  • A direct solution method for pricing options in regime‐switching models
    Math. Financ. (IF 2.25) Pub Date : 2019-07-14
    Masahiko Egami; Rusudan Kevkhishvili

    Pricing financial or real options with arbitrary payoffs in regime‐switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime‐switching models. In this article, we reduce an optimal stopping problem with an arbitrary value function in a two‐regime environment to a pair of optimal stopping

    更新日期:2019-07-14
  • Optimal investment and pricing in the presence of defaults
    Math. Financ. (IF 2.25) Pub Date : 2019-07-12
    Tetsuya Ishikawa; Scott Robertson

    We consider the optimal investment problem with random endowment in the presence of defaults. For an investor with constant absolute risk aversion, we identify the certainty equivalent, and compute prices for defaultable bonds and dynamic protection against default. This latter price is interpreted as the premium for a contingent credit default swap, and connects our work with earlier articles, where

    更新日期:2019-07-12
  • Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets
    Math. Financ. (IF 2.25) Pub Date : 2019-07-11
    Zongxia Liang; Ming Ma

    We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T ] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and

    更新日期:2019-07-11
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