Time-consistent Optimal Portfolio Strategy for Asset-liability Management under Mean-variance Criterion

Chanjuan Li, Zhongfei Li, Ke Fu and Haiqing Song

Accounting and Finance Research, 2013, vol. 2, issue 2, 89

Abstract: This paper studies the time-consistent optimal portfolio strategy of an investor with an exogenous liability. Assume that the investor adopts the mean-variance criterion and trades continuously in a market consisting of one risk-free asset and one risky asset; and the price of the risky asset and the value of the exogenous liability are governed by geometric Brownian motions. An extended Hamilton-Jacobi-Bellman equation is derived, and the analytical expressions of the time-consistent optimal portfolio strategy and the mean-variance efficient frontier are obtained. A numerical example is provided to show the results. Our main findings are- (1) introducing an exogenous liability makes the time-consistent optimal portfolio strategy be a stochastic process; (2) the efficient frontier under the time-consistent optimal strategy for asset-liability management is below both the one under the time-consistent optimal strategy in the case of no liability and the one under the pre-commitment optimal strategy for asset-liability management.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:jfr:afr111:v:2:y:2013:i:2:p:89

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