Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2021, Vol. 38 ›› Issue (6): 778-796.doi: 10.3969/j.issn.1005-3085.2021.06.003

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Optimal Asset Allocation for a DC Pension Fund in the Market with Multiple Dependent Risky Assets

SUN Jingyun1,2,   GUO Jingjun1,   ZHAO Yu1   

  1. 1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020
    2. Center for Quantitative Analysis of Gansu Economic Development, Lanzhou University of Finance and Economics, Lanzhou 730020
  • Online:2021-12-15 Published:2022-02-15
  • Supported by:
    The National Natural Science Foundation of China (71701084; 71961013; 72061020); the Natural Science Foundation of Gansu Province (21JR1RA280); the Innovation Ability Promotion Project for the Higher Education Institutions of Gansu Province (2019A-060); the Project of Silk Road Economic Research Institute in Lanzhou University of Finance and Economics (JYYY201705).

Abstract:

We consider an optimal asset allocation problem for a defined contribution pension fund in the accumulation phase before the participant retired. It is assumed that the prices of $n$ risky assets suffer a common jump phenomenon because of the impact of market systematic risk. So the prices of the risky assets are modeled with dependent jump-diffusion processes. In addition, we suppose that the income process of the participant satisfies a jump-diffusion process before she retired. To minimize the expected square loss between the pension fund account and the expected investment target at the time of retirement, the stochastic dynamic programming method is adopted, and the closed-forms of the optimal investment strategy and the value function are obtained, a verification theorem and its proof are also provided. Finally, through some numerical examples, we find that the jump parameters in the price process of risky asset and participants' income process, the earnings preference of pension fund managers and the expected investment objective process all have significant influence on the optimal investment strategy and the value function.

Key words: defined contribution, dependent jump-diffusion, quadratic loss, Hamilton-Jacobi-Bellman equation

CLC Number: