Time-consistent asset–liability management with imperfect information

This paper investigates time-consistent investment strategies for a multi-period asset–liability management (ALM) problem under the mean–variance criterion. To reflect the reality of incomplete information, the financial market is modeled by a hidden Markov framework that captures both observable and unobservable market states. The returns of risky assets, liabilities, and cash flows are assumed to depend on these states, reflecting the complexities of real-world financial markets. Using the sufficient statistics method, the problem is transformed into one with complete information. Under a non-cooperative game framework, closed-form solutions for the time-consistent ALM strategies, value functions, and efficient frontiers are derived explicitly through the extended Bellman equations and matrix representations. The expectation–maximization (EM) algorithm is employed to estimate hidden Markov model parameters, enhancing the practical applicability of the framework. Numerical examples illustrate the effects of imperfect information, liabilities, and stochastic cash flows on time-consistent investment strategies and efficient frontiers. By addressing the challenges of incomplete information and stochastic dynamics, this study provides actionable insights for designing effective ALM strategies in intricate financial environments.