Insurance, Reinsurance and Dividend Payment

TL;DR

This paper introduces a comprehensive insurance model incorporating reinsurance and dividend payments, analyzing optimal strategies through a controlled jump process and viscosity solutions to Hamilton-Jacobi-Bellman inequalities.

Contribution

It presents a novel stochastic control framework for insurance with reinsurance and dividends, including legislation constraints and a proof of the value function's uniqueness.

Findings

Model captures legislation constraints on contracts

Value function characterized as viscosity solution

Proved uniqueness of the solution

Abstract

The aim of this paper is to introduce an insurance model allowing reinsurance and dividend payment. Our model deals with several homogeneous contracts and takes into account the legislation regarding the provisions to be justified by the insurance companies. This translates into some restriction on the (maximal) number of contracts the company is allowed to cover. We deal with a controlled jump process in which one has free choice of retention level and dividend amount. The value function is given as the maximized expected discounted dividends. We prove that this value function is a viscosity solution of some first-order Hamilton-Jacobi-Bellman variational inequality. Moreover, a uniqueness result is provided.