Optimal Portfolio Decisions in Pension Fund Management

Abstract

This paper analyzes the portfolio problem that the fund manager has to maximize the possibility of reaching his managerial goal before the worst scenario shortfall occurs in the defined benefit pension schemes. The fund ratio process defined as the ratio between the fund level and its liability benchmark is required to maximize the probability that the predetermined target is achieved before it falls below an unacceptable limit. The time-varying opportunity set in our study includes risk-free cash, bonds and stock index. The problems are formulated as a stochastic control framework and solved by dynamic programming techniques. The results show that the optimal portfolio contains the atemporal hedging component minimizing the variation in fund ratio growth, the intertemporal hedging component against changes in the opportunity set and the risk attitude of the fund manager and the state variables risk hedging component. In this study, the adjusted portfolio Sharpe ratio incorporating the correlation structure between risk factors is proposed when there are background risks.