A BSDE-based approach for the optimal reinsurance problem under partial information

TL;DR

This paper develops a BSDE-based method to solve the optimal reinsurance problem under partial information, accounting for unobservable environmental factors affecting claims, and reduces it to a stochastic control problem with full information.

Contribution

It introduces a novel BSDE approach to handle partial information in reinsurance optimization, extending classical methods to infinite-dimensional filtering scenarios.

Findings

Successfully characterizes the value process via BSDEs driven by marked point processes.

Provides a framework for deriving optimal reinsurance strategies under incomplete information.

Bridges the gap between filtering theory and stochastic control in insurance risk management.

Abstract

We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival intensity and claim sizes distribution affected by an unobservable environmental stochastic factor. By filtering techniques (with marked point process observations), we reduce the original problem to an equivalent stochastic control problem under full information. Since the classical Hamilton-Jacobi-Bellman approach does not apply, due to the infinite dimensionality of the filter, we choose an alternative approach based on Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize the value process and the optimal reinsurance strategy in terms of the unique solution to a BSDE driven by a marked point process.