This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to an incomplete financial market consisting of a risk-free asset, a market index with potentially path-dependent, time-varying risk premium and volatility, and a pair of mispriced stocks. The market dynamics are assumed to rely on an affine-form, square-root factor process and the price error is modeled by a co-integrated system. We adopt a backward stochastic differential equation approach hinging on the martingale optimality principle to solve this non-Markovian robust control problem. Closed-form expressions for the robust optimal investment strategies, the probability perturbation process under the well-defined worst-case scenario and the corresponding value function are derived. The admissibility of the robust optimal controls is verified under some technical conditions. Finally, we perform some numerical examples to illustrate the effects of model parameters on the robust investment strategies and draw some economic interpretations from these results.

本文研究了预期效用最大化准则下的鲁棒最优资产负债管理问题。更具体地说，管理者关注潜在的模型不确定性，旨在寻求稳健的最优投资策略。我们纳入了由广义漂移布朗运动描述的不可控随机责任。此外，管理者还可以进入一个不完整的金融市场，该市场由无风险资产、具有潜在路径依赖性、随时间变化的风险溢价和波动性的市场指数以及一对错误定价的股票组成。假设市场动态依赖于仿射形式的平方根因子过程，并且价格误差由协整系统建模。我们采用基于鞅最优原理的后向随机微分方程方法来解决这个非马尔可夫鲁棒控制问题。推导了鲁棒最优投资策略的封闭式表达式、明确定义的最坏情况下的概率扰动过程以及相应的价值函数。在一定的技术条件下验证了鲁棒最优控制的可接受性。最后，我们通过一些数值例子来说明模型参数对稳健投资策略的影响，并从这些结果中得出一些经济解释。推导了明确定义的最坏情况下的概率扰动过程以及相应的价值函数。在一定的技术条件下验证了鲁棒最优控制的可接受性。最后，我们通过一些数值例子来说明模型参数对稳健投资策略的影响，并从这些结果中得出一些经济解释。推导了明确定义的最坏情况下的概率扰动过程以及相应的价值函数。在一定的技术条件下验证了鲁棒最优控制的可接受性。最后，我们通过一些数值例子来说明模型参数对稳健投资策略的影响，并从这些结果中得出一些经济解释。