Relative Performance Concern on DC Pension Plan under Heston Model with Inflation Risk

Aimin Song,Peimin Chen,Michele Guida

doi:10.1155/2020/5180286

Abstract

With the global outbreak of new coronavirus pneumonia, more and more countries have entered the state of sealing off cities. After the epidemic, with the shortage of some materials, the economy is very likely to enter the state of inflation. Thereby, it is necessary and urgent for us to reconsider investment problems involving inflation risk. In this paper, we mainly study the optimal investment strategy of two defined contribution (DC) pension managers with strategy interaction under inflation risk. The traditional portfolio literatures mainly focus on DC pension plan and try to maximize the expected utility of terminal nominal wealth. In this paper, we consider the more complicated situation that pension managers have, both concerns on relative wealth and relative risk aversion. Then, the objective function is constructed to satisfy these two concerns. The dynamic programming principle method is employed to solve the above problems, and a series of analytical solutions to this problem are obtained. Finally, some numerical examples are discussed for the economic implications to support our theoretical results.

Highlights

As a continuous increase in the average life expectancy of human beings, the optimal portfolio strategies of pension funds have been continuously studied in the literature
One is the defined benefit (DB) pension plan, in which people do not need to consider the pension’s investment portfolio and longevity risks and enjoy a fixed benefit after retirement. e other one is the defined contribution (DC) pension plan, in which workers pay their pensions at a certain rate of their salary before retirement
Compared with the DB pension plan, DC pension plan relieves the pressure on the social security system by shifting investment risk and longevity risk from sponsors to pension plan members

Summary

Introduction

As a continuous increase in the average life expectancy of human beings, the optimal portfolio strategies of pension funds have been continuously studied in the literature. Espinosa and Touzi [13] consider a continuous time stochastic dynamic model and the optimal investment strategy of two investors with relative wealth concern. E literature above only assume that the investors are only concerned about the relative wealth about their competitors, but in real investment, markets investors care about this point and are affected by the risk aversion of competitors. By the DPP method and the corresponding HJB equation, we obtain the explicit solution of the optimal portfolio strategies of RPC manager and the specific solution for the cases of RWC and RRAC, respectively.

Mathematical Models

The Competition Model