Open AccessTime-consistent Optimal Portfolio Strategy for Asset-liability Management under Mean-variance Criterion
Author(s) -
LI Chanjuan,
Zhongfei Li,
Ke Fu,
H. Song
Publication year - 2013
Publication title -
accounting and finance research
Language(s) - English
Resource type - Journals
eISSN - 1927-5994
pISSN - 1927-5986
DOI - 10.5430/afr.v2n2p89
Subject(s) - efficient frontier , portfolio , liability , asset (computer security) , replicating portfolio , economics , variance (accounting) , post modern portfolio theory , actuarial science , geometric brownian motion , project portfolio management , microeconomics , econometrics , portfolio optimization , financial economics , computer science , finance , diffusion process , computer security , accounting , economy , management , project management , service (business)
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