A Random Parameter Model for Continuous-Time Mean-Variance Asset-Liability Management

Abstract EN

We consider a continuous-time mean-variance asset-liability management problem in a market with random market parameters; that is, interest rate, appreciation rates, and volatility rates are considered to be stochastic processes.

By using the theories of stochastic linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), we tackle this problem and derive optimal investment strategies as well as the mean-variance efficient frontier analytically in terms of the solution of BSDEs.

We find that the efficient frontier is still a parabola in a market with random parameters.

Comparing with the existing results, we also find that the liability does not affect the feasibility of the mean-variance portfolio selection problem.

However, in an incomplete market with random parameters, the liability can not be fully hedged.