Portfolio optimization under the stochastic elasticity of variance

Sung Jin Yang, Min Ku Lee, Jeong Hoon Kim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Based on the observation that the elasticity of variance of risky assets is randomly varying around a constant, we take an underlying asset model in which the averaged constant elasticity of variance is perturbed by a small fast fluctuating process and study the Merton type portfolio optimization problem using dynamic programming as well as asymptotic expansions. The Hamilton-Jacobi-Bellman equation for each of the power and exponential utility functions leads to an optimal trading strategy as a perturbation around the well known one. We reveal the impact of both the constant elasticity of variance upon the Merton investment optimal control under the Black-Scholes model and the stochastic elasticity of variance upon the investment optimal control under the constant elasticity of variance model. The concavity of the investment policy with respect to the excess return is characteristic of a market economy with the constant or stochastic elasticity of variance.

Original languageEnglish
Article number1350024
JournalStochastics and Dynamics
Volume14
Issue number3
DOIs
Publication statusPublished - 2014 Sep

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Portfolio Optimization
Elasticity
Optimal Control
Exponential Utility
Black-Scholes Model
Trading Strategies
Hamilton-Jacobi-Bellman Equation
Concavity
Optimal Strategy
Utility Function
Dynamic programming
Dynamic Programming
Excess
Asymptotic Expansion
Optimization Problem
Perturbation
Model

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation

Cite this

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Portfolio optimization under the stochastic elasticity of variance. / Yang, Sung Jin; Lee, Min Ku; Kim, Jeong Hoon.

In: Stochastics and Dynamics, Vol. 14, No. 3, 1350024, 09.2014.

Research output: Contribution to journalArticle

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