Optimal Control of Stochastic Functional Differential Equations with Application to Finance
Edson A. Coayla-Teran, Anatoly Swishchuk
TL;DR
This paper develops a framework for optimal control of stochastic functional differential equations using HJB equations, with applications to financial portfolio optimization.
Contribution
It introduces a novel approach to control SFDEs via HJB equations and demonstrates its application in finance, specifically in portfolio selection.
Findings
Derived HJB and converse HJB equations for SFDEs
Applied the framework to optimal portfolio selection
Provided mathematical finance applications
Abstract
This work is devoted to the study of optimal control of stochastic functional differential equations (SFDEs) and its application to mathematical finance. By using the Dynkin formula and solution of the Dirichlet-Poisson problem, the Hamilton-Jacobi-Bellman (HJB) equation and the converse HJB equation are derived. Furthermore, applications are given to an optimal portfolio selection problem.
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Taxonomy
TopicsStochastic processes and financial applications · Fuzzy Systems and Optimization · Complex Systems and Time Series Analysis