This paper is devoted to the study of an optimal investment and risk control problem for an insurer. The risky asset process and the insurance liability process are governed by stochastic differential equations with jumps and anticipative parameters. The insurer can only get access to partial information about the financial market and the insurance business to make decisions. Taking into account endogenous and exogenous factors, we assume the time horizon is uncertain. With the aim of expected logarithmic utility maximization, we adopt the forward stochastic calculus and the Malliavin calculus to derive a characterization of the optimal strategy. In some particular cases, we obtain the optimal strategies in closed-form and get some new insights.

本文致力于研究保险公司的最优投资和风险控制问题。风险资产过程和保险责任过程由具有跳跃和预期参数的随机微分方程控制。保险公司只能获得有关金融市场和保险业务的部分信息来做出决策。考虑到内生和外生因素，我们假设时间范围是不确定的。以期望对数效用最大化为目标，我们采用前向随机演算和 Malliavin 演算来推导最优策略的表征。在某些特定情况下，我们获得了封闭形式的最优策略并获得了一些新的见解。