Portfolio and reinsurance optimization under unknown market price of risk

TL;DR

This paper develops a framework for optimal investment and reinsurance strategies for insurance companies with partial information on market risk, providing explicit solutions and analyzing the value of information through numerical experiments.

Contribution

It introduces a filtering-based approach to solve the partial information portfolio and reinsurance optimization problem, deriving explicit formulas for strategies and value functions.

Findings

Explicit formulas for optimal strategies under partial information

Comparison of strategies between partially and fully informed insurers

Numerical evaluation of the value of information

Abstract

We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving different filtrations, into an equivalent stochastic control problem under the observation filtration only, the so-called separated problem. The Markovian structure of the separated problem allows us to apply a classical approach to stochastic optimization based on the Hamilton-Jacobi-Bellman equation, and to provide explicit formulas for the value function and the optimal investment-reinsurance strategy. We finally discuss some comparisons between the optimal strategies pursued by a partially informed insurer and that followed by a fully informed insurer, and we evaluate the value of information using the idea of indifference pricing. These results are also supported by numerical experiments.