Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost

Yuri F. Saporito

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arXiv · 1611.00589

Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost

Yuri F. Saporito

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Abstract

In this paper, we consider the functional It\^o calculus framework to find a path-dependent version of the Hamilton-Jacobi-Bellman equation for stochastic control problems that feature dynamics and running cost that depend on the path of the control. We also prove a Dynamic Programming Principle for such problems. We apply our results to path-dependence of the delay type. We further study Stochastic Differential Games in this context.

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Yuri F. Saporito. 2016-11-02. Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost. https://arxiv.org/abs/1611.00589

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