Optimal tactics in community pension model for defined benefit pension plans

Against the backdrop of an aging population, community pension initiatives are gaining traction, permeating societal landscapes. This study delves into the equilibrium strategy within the context of a defined benefit pension plan, employing a differential game framework with a community pension model. Hence, the model entails the company's controls over investment rates in funds, juxtaposed with employees' inclination towards a greater proportion of community pension allocation in said funds. To tackle this issue, a stochastic differential game model for pensions under a community pension scheme is formulated. Leveraging the Hamilton-Jacobi-Bellman equation, we derive the Markov Perfect Nash Equilibrium solution and optimal portfolio. Through numerical simulations, we analyze the impact of varying risk aversion levels across different parameter values on equilibrium ratios, thereby offering insights into managerial risk tolerance.