Abstract: This paper focuses on an asset-liability management problem for an investor who can invest in a risk-free asset and a risky asset whose price process is described by the Heston model, while the liability process is described by a Brownian motion with drift. The objective of the Ambiguity-Averse Investor (AAI) is to find a robust optimal investment strategy under the mean-variance criterion. By applying stochastic control theory, a verification theorem is provided and proved and the corresponding extended HJB equation is established. Furthermore, the robust equilibrium investment strategy and the corresponding equilibrium value function are derived by solving the extended HJB equation. Finally, numerical examples are also provided to illustrate how the optimal robust investment strategy changes and utility improvement when some model parameters vary. Our main findings are: (1) when the correlation coefficient between the price of risky assets and its variance is non-negative number, the bigger the fluctuation of stock variance, the more disadvantageous investment. (2) when the correlation coefficient between the price of risky assets and its variance greater, the risk of risky assets is greater, and investors will adopt a conservative investment strategy. (3) when investors have more debt, they hedge their bets by investing in riskier assets. (4) ignoring model uncertainty leads to significant utility loss for the AAI. These result analyses reveal some interesting phenomena and provide useful guidance for optimal investment of asset-liability management in reality.

Key words: time-consistent, robust strategy, asset-liability, portfolio