Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models
Optimization and Control
2023-02-20 v1 Analysis of PDEs
Mathematical Finance
Abstract
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we characterize the value function of the problem as the unique viscosity solution of the associated infinite-dimensional Hamilton-Jacobi-Bellman equation. Finally, we prove a -partial regularity of the value function. We apply these results to path dependent financial and economic problems (Merton-like portfolio problem and optimal advertising).
Keywords
Cite
@article{arxiv.2302.08809,
title = {Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models},
author = {Filippo de Feo and Salvatore Federico and Andrzej Święch},
journal= {arXiv preprint arXiv:2302.08809},
year = {2023}
}