An optimal consumption model with stochastic volatility
An extension of the classical Merton optimal investment-consumption model is considered in which volatility of the risky asset is stochastic. The goal is to choose consumption and investment controls which maximize total expected discounted HARA utility of consumption. Stochastic volatility enters via dependence on an economic factor \(Y_t\) of the correlation \(\sigma(Y_t)\) in the risky asset price dynamics. The factor \(Y_t\) is an ergodic Markov diffusion process involving a Brownian motion. The prices of the shares in the risky asset also fluctuate according to a diffusion process involving another, possibly correlated, Brownian motion. The dynamic programming method is used to analyze this portfolio optimization problem. Writing the value function in a special form, one can see that another optimal control problem is involved and studying its associated HJB equation, smoothness properties of the original value function are derived as well as optimal policies.
scientific article; zbMATH DE number 2059108