Optimal investment of DC pension plan with two VaR constraints

Abstract

In this paper, we investigate an optimal investment problem under two value-at-risk (VaR) constraints faced by a defined contribution (DC) pension fund manager. We apply a concavification technique and a Lagrange dual method to solve the problem and derive the closed-form representations of the optimal wealth and portfolio processes in terms of the state price density. Theoretical and numerical results show that the two VaR constraints can significantly impact the distribution of the optimal terminal wealth.

Keywords:

• DC pension plan
• utility maximization
• two VaR constraints
• martingale approach
• Lagrange dual method
• concavification

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 91B16
• 91G10

Additional information

Funding

The research of Yinghui Dong was supported by Humanities and Social Science Research Projects in Ministry of Education [20YJAZH025], the NSF of Jiangsu Province [Grant No. BK20170064], the NNSF of China [Grant No. 11771320], and QingLan Project and Suzhou Key Laboratory for Big Data and Information Service [SZS201813].