Controlled Continuous Time Random Walks and fractional Hamilton Jacobi Bellman equations

TL;DR

This paper investigates controlled continuous time random walks and derives fractional Hamilton-Jacobi-Bellman equations as their limiting dynamic programming equations, extending previous results to a controlled framework.

Contribution

It introduces a controlled setting for CTRWs and heuristically derives fractional HJB equations, expanding the theoretical understanding of stochastic control in anomalous diffusion models.

Findings

Derivation of fractional HJB equations from controlled CTRWs

Extension of previous results to controlled stochastic processes

Heuristic approach to linking CTRWs with fractional PDEs

Abstract

In this paper we study controlled continuous time random walks (CTRWs) and heuristically derive pay-off function dynamic programming (DP) equations which turn in the limit of standard scaling to fractional Hamilton Jacobi Bellman type equations. This paper aims to extend results from [1] in a controlled setting.