Portfolio optimization for pension plans under hybrid stochastic and local volatility

Abstract

Based upon an observation that it is too restrictive to assume a definite correlation of the underlying asset price and its volatility, we use a hybrid model of the constant elasticity of variance and stochastic volatility to study a portfolio optimization problem for pension plans. By using asymptotic analysis, we derive a correction to the optimal strategy for the constant elasticity of variance model and subsequently the fine structure of the corrected optimal strategy is revealed. The result is a generalization of Merton’s strategy in terms of the stochastic volatility and the elasticity of variance.