An optimal consumption model with stochastic volatility
type: Item
instance of: scholarly article
title: An optimal consumption model with stochastic volatility
zbMATH Open document ID: 1035.60028
author: Wendell Fleming
author: Daniel Hernández-Hernández
published in: Finance and Stochastics
publication date: 2004-03-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 91B70
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 2059108
zbMATH Keywords: stochastic volatility
zbMATH Keywords: portfolio optimization
zbMATH Keywords: factor modelling
zbMATH Keywords: mean reverting
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s007800200083
OpenAlex ID: W2049388336
DOI: 10.1007/S007800200083
description: scientific article; zbMATH DE number 2059108