Portfolio Optimization & Stochastic Volatility Asymptotics

Forthcoming in Mathematical Finance

37 Pages Posted: 30 Jul 2014 Last revised: 3 Jul 2015

See all articles by Jean-Pierre Fouque

Jean-Pierre Fouque

University of California, Santa Barbara (UCSB) - Statistics & Applied Probablity

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Thaleia Zariphopoulou

University of Texas at Austin - Red McCombs School of Business

Date Written: March 14, 2013

Abstract

We study the Merton portfolio optimization problem in the presence of stochastic volatility using asymptotic approximations when the volatility process is characterized by its time scales of fluctuation. This approach is tractable because it treats the incomplete markets problem as a perturbation around the complete market constant volatility problem for the value function, which is well-understood. When volatility is fast mean-reverting, this is a singular perturbation problem for a nonlinear Hamilton-Jacobi-Bellman PDE, while when volatility is slowly varying, it is a regular perturbation. These analyses can be combined for multifactor multiscale stochastic volatility models. The asymptotics shares remarkable similarities with the linear option pricing problem, which follows from some new properties of the Merton risk-tolerance function.

We give examples in the family of mixture of power utilities and also we use our asymptotic analysis to suggest a "practical" strategy which does not require tracking the fast-moving volatility. In this paper, we present formal derivations of asymptotic approximations, and we provide a convergence proof in the case of power utility and single factor stochastic volatility. We assess our approximation in a particular case where there is an explicit solution.

Keywords: portfolio optimization, stochastic volatility, asymptotic analysis

Suggested Citation

Fouque, Jean-Pierre and Sircar, Ronnie and Zariphopoulou, Thaleia, Portfolio Optimization & Stochastic Volatility Asymptotics (March 14, 2013). Forthcoming in Mathematical Finance, Available at SSRN: https://ssrn.com/abstract=2473289 or http://dx.doi.org/10.2139/ssrn.2473289

Jean-Pierre Fouque

University of California, Santa Barbara (UCSB) - Statistics & Applied Probablity ( email )

United States

Ronnie Sircar (Contact Author)

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

Thaleia Zariphopoulou

University of Texas at Austin - Red McCombs School of Business ( email )

Austin, TX 78712
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
180
Abstract Views
1,040
Rank
256,323
PlumX Metrics