Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate

Abstract

In this paper, we investigate a multi-period mean-variance assetliability management problem with stochastic interest rate and seek its time-consistent strategy. The financial market is assumed to be composed of one risk-free asset and multiple risky assets, and the stochastic interest rate is characterized by the discrete-time Vasicek model proposed by Yao et al. (2016a)[38]. We regard this problem as a non-cooperative game whose equilibrium strategy is the desired time-consistent strategy. We derive the analytical expressions of the equilibrium strategy, the equilibrium value function and the equilibrium efficient frontier by the extended Bellman equation. Some special cases of our model are discussed, and some properties of our equilibrium strategy, including a two-fund separation theorem, are proposed. Finally, a numerical example with real data is given to illustrate our theoretical results.