Utility maximization in models with conditionally independent increments

TL;DR

This paper addresses utility maximization in financial models with stochastic factors, deriving optimal strategies under the assumption of conditionally independent asset price increments using martingale methods.

Contribution

It introduces a novel approach to solve utility maximization problems with conditionally independent increments via martingale techniques and conditioning arguments.

Findings

Derived explicit optimal strategies for power utility

Extended the utility maximization framework to models with stochastic factors

Provided conditions under which the strategies are optimal

Abstract

We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption that the increments of the asset price are independent conditionally on the factor process.