Optimal investment and consumption for Ornstein-Uhlenbeck spread financial markets with logarithmic utility

TL;DR

This paper derives explicit optimal investment and consumption strategies in a spread market modeled by an Ornstein-Uhlenbeck process with logarithmic utility, using stochastic control and numerical analysis.

Contribution

It provides an explicit solution to the HJB equation and constructs optimal strategies for a spread market modeled by OU process, with a verification theorem and numerical simulations.

Findings

Explicit optimal strategies derived for OU spread market

Verification theorem established for the control problem

Numerical simulations illustrate the strategies' performance

Abstract

We consider a spread financial market defined by the multidimensional Ornstein--Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions in the base of stochastic dynamical programming method. We show a special Verification Theorem for this case. We find the solution to the Hamilton--Jacobi--Bellman (HJB) equation in explicit form and as a consequence we construct the optimal financial strategies. Moreover, we study the constructed strategy by numerical simulations.