Portfolio selection and risk control for an insurer with uncertain time horizon under inside information

This paper is devoted to studying the optimal investment and risk control strategy for an insurer with uncertain time under inside information. The jump process is incorporated into our research framework, and the correlation between the risky asset and the risk process is considered. Assuming the exit time is uncertain, we use forward calculus and Malliavin calculus to derive a characterization of the optimal investment and risk control under the criterion of maximizing the logarithmic utility of the terminal wealth in a pure jump market and a mixed market. Moreover, we apply filtration enlargement techniques to several interesting special cases and derive the corresponding explicit solutions. Finally, we conduct numerical simulations to analyze the impact of correlation coefficient and insider information on the investment strategy.