Robust equilibrium strategy in DB pension plans with Poisson jump

The robust non-cooperative game problem in a defined-benefit pension plan with excess funds with Poisson jumps is studied. Corporate managers are concerned about the investment performance of the fund's surplus, and pension participants demand a share of the fund's surplus. The price of risk assets in financial market is described by the diffusion process with Poisson jump, and the probability model in financial market is assumed to be uncertain. Suppose that corporate managers and pension participants are ambiguous averse. Based on the robust control strategy, the pension participant's goal is to maximize the expected discounted utility of the benefit, and the firm's goal is to seek to maximize the utility of the fund's surplus. By using robust control theory, we get robust equilibrium investment and benefit strategies under non-cooperative game. Finally, numerical results are used to explain the economic behavior of robust strategies in the game.