Forward-backward systems for expected utility maximization
نویسندگان
چکیده
In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE). AMS Subject Classification: Primary 60H10, 93E20 JEL Classification: C61, D52, D53
منابع مشابه
Simulation-Based Sequential Bayesian Design
We consider simulation-based methods for exploration and maximization of expected utility in sequential decision problems. We consider problems which require backward induction with analytically intractable expected utility integrals at each stage. We propose to use forward simulation to approximate the integral expressions, and a reduction of the allowable action space to avoid problems relate...
متن کاملMaximum Principles of Markov Regime-Switching Forward-Backward Stochastic Differential Equations with Jumps and Partial Information
Résumé/Abstract: In this talk, we present three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for optimal control for a system driven by a Markov regime-switching forward and backward jump-diffusion model is developed. After, an equi...
متن کاملBACKWARD STOCHASTIC PDEs RELATED TO THE UTILITY MAXIMIZATION PROBLEM
We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an R-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial differential equation (BSPDE) related directly to the primal problem and show th...
متن کاملMaximization of Recursive Utilities: A Dynamic Maximum Principle Approach
In this paper we study a class of robust utility maximization problem over a terminal wealth and consumption in a complete market. Using the backward stochastic differential equation theory (BSDE in short), we derive a comparison theorem to give a dynamic maximum principle for the optimal control of our problem. We prove the existence and uniqueness of an optimal strategy and we characterize it...
متن کاملMarket Completion and Robust Utility Maximization
In this thesis we study two problems of financial mathematics that are closely related. The first part proposes a method to find prices and hedging strategies for risky claims exposed to a risk factor that is not hedgeable on a financial market. In the second part we calculate the maximal utility and optimal trading strategies on incomplete markets using Backward Stochastic Differential Equatio...
متن کامل