Abstract:

Inflation risk is one of the most direct and important influential factors in the process of pension fund scheme management. In this paper, inflation risk is supposed to be measured by price index satisfying geometric Brownian motion. And instantaneous expected inflation rate is assumed to be driven by Ornstein-Uhlenbeck process. The fund manager plans to invest his real wealth in the financial market composed of multiple risky assets and expect to maximize expected utility of terminal real wealth. His goal is to obtain the optimal investment strategy for defined contribution pension fund scheme in the accumulation phase. Hyperbolic absolute risk aversion (HARA) utility function is of general utility framework and consists of power utility, exponential utility and logarithmic utility as specific cases. This paper supposes the risky aversion degree of fund manager to satisfy HARA utility and uses stochastic dynamic programming principle along with Legendre transform-dual theory to successfully obtain the closed-form expression of the optimal investment strategy. In addition, some special cases are derived in detail.

Key words: inflation risk, DC pension fund scheme, HARA utility, Legendre transform-dual theory, optimal investment strategy