Robust optimal investment and risk control for an insurer with general insider information

TL;DR

This paper develops a robust framework for optimal investment and risk management for insurers with general insider information, considering model uncertainty and jump diffusion processes, providing explicit solutions for different insurer sizes.

Contribution

It introduces a novel approach using forward integrals and stochastic maximum principle to characterize optimal strategies under broad insider information and model uncertainty.

Findings

Closed-form solutions for small insurer in continuous case.

Half closed-form solutions with jumps.

Reduction to quadratic BSDE for large insurer.

Abstract

In this paper, we study the robust optimal investment and risk control problem for an insurer who owns the insider information about the financial market and the insurance market under model uncertainty. Both financial risky asset process and insurance risk process are assumed to be very general jump diffusion processes. The insider information is of the most general form rather than the initial enlargement type. We use the theory of forward integrals to give the first half characterization of the robust optimal strategy and transform the anticipating stochastic differential game problem into the nonanticipative stochastic differential game problem. Then we adopt the stochastic maximum principle to obtain the total characterization of the robust strategy. We discuss the two typical situations when the insurer is `small' and `large' by Malliavin calculus. For the `small' insurer, we obtain the closed-form solution in the continuous case and the half closed-form solution in the case with jumps. For the `large' insurer, we reduce the problem to the quadratic backward stochastic differential equation (BSDE) and obtain the closed-form solution in the continuous case without model uncertainty. We discuss some impacts of the model uncertainty, insider information and the `large' insurer on the optimal strategy.