Optimal investment strategy for DC pension with mean-weighted variance-CVaR criterion under partial information

Abstract

This paper studies an asset allocation problem of defined contribution (DC) pension with partial observation and minimum guarantee constraint. In the general framework of the financial market, the investment optimization problem under partial information is transformed into the problem under complete information by using the measure transformation approach. Then two auxiliary processes are introduced to tackle the non-self-financing property of the wealth process. With the mean-weighted variance-CVaR criterion, the optimal terminal surplus and the optimal investment strategy are derived by the martingale method. In order to obtain the concrete expression of the optimal investment strategy, we focus on a particular financial market where three kinds of assets are available, including the risk-free asset, the zero coupon bond and the stock. We assume that the return rate is modulated by a hidden Markov chain and the interest rate is described by the Vasicek model. The analytical expression of the optimal investment strategy is derived by adopting the Wonham filter theory and the Malliavin calculus. Finally, the numerical analysis related to the optimal terminal wealth, the optimal investment strategy and the values of risk measures is carried out to illustrate the theoretical results.