Summary: It is often the case that some unexpected event may force an investor to terminate her investment and leave the market. We consider in this paper the mean-variance formulation of multi-period portfolio optimization for asset-liability management with an uncertain investment horizon. Under the assumption that exit time follows a given distribution, the problem under investigation with uncertain investment horizon can be translated into one with deterministic exit time. By making use of the embedding technique of D. Li
and W.-L. Ng
[Math. Finance 10, 387–406 (2000; Zbl 0997.91027
)], we derive an analytical optimal strategy and an analytical expression of the mean-variance efficient frontier for the mean-variance formulation of the problem.