Optimal Investment for the Defined-contribution Pension Based on Non-extensive Statistical Mechanics and Exponential Utility Function

Under the framework of non-extensive statistical mechanics, the optimal fund allocation of pension is studied by maximizing the expected utility of terminal wealth. In order to accurately approximate the actual financial market, the non-extensive statistical theory is employed to model prices of the risky asset, which can describe the high peak and fat tail characteristics of returns. Based on the criterion of maximizing the expected utility of terminal wealth, the Hamilton–Jacob–Bellman equation is established under the condition of the exponential utility function. Furthermore, using the duality theory, an analytical solution for the optimal investment strategy is obtained. Finally, the influence of the main model parameters on the optimal investment strategy is analyzed through numerical methods. Abstract Published by the Jagiellonian University 2025 authors