Nash equilibrium strategies for a defined contribution pension management |
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| Institution: | 1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, PR China;2. Department of Economics and International Trade, Guangdong University of Finance, Guangzhou 510521, PR China;3. School of Insurance, Central University of Finance and Economics, Beijing 100081, PR China;1. Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel;2. Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, United Kingdom;1. School of Risk Management, Insurance, and Actuarial Science, St. John’s University, United States;2. Insurance/Risk Management & Business Economics/Policy, University of Pennsylvania - The Wharton School, United States;1. Department of Mathematics and Statistics, York University, Toronto, Canada;2. Schulich School of Business, Finance Area, York University, Toronto, Canada;1. Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada;1. Towers Watson Research and Innovation Center, Youkeyuan Road 88, 430074, Wuhan, China;2. SAV, Swiss certified pension actuary, Switzerland;3. Towers Watson AG, Talstrasse 62, 8021 Zurich, Switzerland |
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| Abstract: | This paper studies the time-consistent investment strategy for a defined contribution (DC) pension plan under the mean–variance criterion. Since the time horizon of a pension fund management problem is relatively long, two background risks are taken into account: the inflation risk and the salary risk. Meanwhile, there are a risk-free asset, a stock and an inflation-indexed bond available in the financial market. The extended Hamilton–Jacobi–Bellman (HJB for short) equation of the equilibrium value function and the verification theorem corresponding to our problem are presented. The closed-form time-consistent investment strategy and the equilibrium efficient frontier are obtained by stochastic control technique. The effects of the inflation and stochastic income on the equilibrium strategy and the equilibrium efficient frontier are illustrated by mathematical and numerical analysis. Finally, we compare in detail the time-consistent results in our paper with the pre-commitment one and find the distinct properties of these two results. |
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| Keywords: | Defined contribution Stochastic inflation Stochastic salary Nash equilibrium strategy Mean–variance |
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