Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns |
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| Institution: | 1. School of Mathematical Sciences, Peking University, Beijing 100871, PR China;2. Key Laboratory of Mathematical Economics and Quantitative Finance, Peking University, Beijing 100871, PR China;1. Department of Finance and Insurance, Lingnan University, 8 Castle Peak Road, Tuen Mun, Hong Kong;2. Department of Risk Management and Insurance, Georgia State University, 35 Broad Street (11th Floor), Atlanta, GA 30309, USA;1. Department of Mathematics and Statistics, York University, Toronto, Canada;2. Schulich School of Business, Finance Area, York University, Toronto, Canada;1. School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China;2. Department of Economics, The University of Melbourne, Parkville, Victoria 3010, Australia;3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong;1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, PR China;2. Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, PR China |
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| Abstract: | This paper studies the optimization problem of DC pension plan under mean–variance criterion. The financial market consists of cash, bond and stock. Similar to Guan and Liang (2014), we assume that the instantaneous interest rate is an affine process including the Cox–Ingersoll–Ross (CIR) model and Vasicek model. However, we assume that the expected return of the stock follows a completely different mean-reverting process, which can well display the bear and bull features of the market, and the market price of the stock index is the Ornstein–Uhlenbeck process. The pension manager thus has to undertake the risks of interest rate and market price of stock index. Besides, a special stochastic contribution rate is formulated. The goal of the pension manager is to maximize the expected terminal value and minimize the variance of terminal value. We will use the technique developed by Guan and Liang (2014) to tackle this problem and derive the closed-forms of efficient frontier and strategies. Numerical analysis is given in the end of this paper to show the economic behavior of the efficient frontier and strategies. |
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| Keywords: | Defined contribution pension plan Stochastic interest rate Mean-reverting returns Stochastic market price of risk Mean–variance efficiency Stochastic dynamic programming |
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