Robust portfolio choice for a DC pension plan with inflation risk and mean-reverting risk premium under ambiguity

Abstract

This paper investigates a robust optimal portfolio choice problem for a defined contribution (DC) pension plan member. The member worries about model ambiguity and aims to seek robust optimal investment strategies. Specifically, the member has a stochastic salary, considers inflation risk and invests her pension account wealth into a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock whose expected return rate follows a mean-reverting process. By using the dynamic programming approach, the robust optimal investment strategy and the corresponding value function are explicitly derived, and subsequently a verification theorem is provided. Furthermore, two special cases of our portfolio model are discussed. Finally, a numerical example is presented to reveal economic implications of our theoretical results and to illustrate the effects of the model parameters on the robust optimal investment strategy. We find that ambiguity about the dynamics of the inflation-indexed bond price and the stock price and expected return rate has different influences on the robust optimal investment strategy, and that neglecting ambiguity will always lead to utility loss.