Bayesian adaptive portfolio optimization for DC pension plans

Abstract

This paper investigates an optimally defined contribution (DC) pension fund problem with partial information. The fund manager invests his wealth in a financial market consisting of a risk-free asset, a stock, and an index bond. He aims to maximize the expected utility of the terminal wealth minus the minimum guarantee. The drift terms of the stock and the index bond are represented by unobservable random variables and the market price of risk follows a prior probability distribution. Using the Bayesian approach and filtering theory, we first transform the original unobservable optimization problem into one with full information. After that, we introduce an auxiliary process to convert the full information problem into an equivalent unconstrained self-financing optimization problem. We then solve the problem and obtain an explicit expression for the optimal investment strategy by using the martingale approach. To compare the results, we also derive the optimal investment strategy for the DC pension model under constant relative risk aversion (CRRA) utility in which the financial market is fully observable.