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Mean field and n-player games in Ito-diffusion markets under forward performance criteria

Probability, Uncertainty and Quantitative Risk 2024年第2期9卷 123-148页

作者： Thaleia Zariphopoulou Departments of Mathematics and IROM McCombs School of BusinessThe University of Teras at AustinAustinTX 78712USA Oaford-Man Institute of Quantitative Finance University of OafordOrfordOX26EDUK

We study n-player games of portfolio choice in general common Ito-diffusion markets under relative performance criteria and time monotone forward ***,also,consider their continuum limit which gives rise to a forward mean field game with unbounded controls in both the drift and volatility ***,we allow for general(time monotone)preferences,thus departing from the homothetic case,the only case so far *** produce explicit solutions for the optimal policies,the optimal wealth processes and the game values,and also provide representative examples for both the finite and the mean field game.

关键词： Mean field game n-player game Ito-diffusion forward performance criteria

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Rank-dependent ppredictableforward performance processes

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Probability, Uncertainty and Quantitative Risk 2024年第2期9卷 181-218页

作者： Bahman Angoshtari Shida Duan Department of Mathematics University of MiamiCoral Gables FL 33146USA

Predictable forward performance processes(PFPPs)are stochastic optimal control frameworks for an agent who controls a randomly evolving system but can only prescribe the system dynamics for a short period *** is a common scenario in which a controlling agent frequently re-calibrates her *** introduce a new class of PFPPs based on rank-dependent utility,generalizing existing models that are based on expected utility theory(EUT).We establish existence of rank-dependent PFPPs under a conditionally complete market and exogenous probability distortion functions which are updated *** show that their construction reduces to solving an integral equation that generalizes the integral equation obtained under EUT in previous *** then propose a new approach for solving the integral equation via theory of Volterra *** illustrate our result in the special case of conditionally complete Black-Scholes model.

关键词： forward performance criteria Rank dependent utility Probability distortion Time consistency Inverse investment problems Volterra integral equations Completely monotonic inverse marginals

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