Optimal Investment and Consumption for Multidimensional Spread Financial Markets with Logarithmic Utility

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 using a 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 optimal financial strategies. Moreover, we study the constructed strategies with numerical simulations.

Keywords

• optimality
• Feynman–Kac mapping
• Hamilton–Jacobi–Bellman equation
• Itô formula
• Brownian motion
• Ornstein–Uhlenbeck processes