A stochastic Nash equilibrium portfolio game between two DC pension funds

- Study stochastic Nash equilibrium portfolio game of two DC pension funds.
- Derive closed-forms of the Nash equilibrium portfolio strategies.
- Give numerical analysis to investigate evolutions of the Nash equilibrium strategies.

In this paper, we study the stochastic Nash equilibrium portfolio game between two pension funds under inflation risks. The financial market consists of cash, bond and two stocks. It is assumed that the price index is derived through a generalized Fisher equation while the bond is related to the price index to hedge the risk of inflation. Besides, these two pension managers can invest in their familiar stocks. The goal of the pension managers is to maximize the utility of the weighted terminal wealth and relative wealth. Dynamic programming method is employed to derive the Nash equilibrium strategies. In the end, a numerical analysis is presented to reveal the economic behaviors of the two DC pension funds.