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Optimal management of DB pension fund with the possibilities of both underfunded and overfunded cases

Abstract

This work investigates the optimal management of an aggregated defined pension plan in a stochastic environment. The interest rate is supposed to follow the Ornstein-Uhlenbeck model. The benefits follow the geometric Brownian motion while the contribution rate is determined by the spread method of fund amortization. The pension manager invests in the financial market with three assets: cash, bond and a stock. Regardless of the initial status of the plan, we suppose that the pension fund may become underfunded or overfunded at the terminal time. The optimization goal of the manager is to maximize the expected utility in the overfunded region minus the weighted solvency risk in the underfunded region. Based on theory of derivative pricing, we introduce an auxiliary process and related equivalent optimization problem. Using martingale method, four cases (high tolerance towards solvency risk, low tolerance towards solvency risk, extreme risk aversion and no solution) for the optimal wealth process, optimal portfolio, efficient frontier and probabilities in the overfunded (underfunded) are obtained. In the end of the paper, numerical analyses are present to illustrate the manager's economic behaviors.


个人简介:关国卉,中国人民大学统计学院副教授,应用统计科学研究中心研究员。主要研究领域包括最优再保险,最优资产配置和养老金管理等。在Insurance: Mathematics and Economics、Scandinavian Actuarial Journal、Journal of Computational and Applied Mathematics、数理统计与管理等期刊发表多篇论文,主持国家自科青年项目,博士后基金面上一等资助等。