Dynamic Set-Up for Designing Optimal Reinsurance Contracts

In this paper, we consider a dynamic set-up for designing optimal reinsurance contracts. The main objective is to maximise the lifetime dividends of an insurance company. We study three problems. First, we consider a general dividend maximisation problem with just budget constraints; second, we add solvency conditions to the previous problem; and finally, we consider a problem with solvency constraints and a particular type of dividend functions. We show that the optimal solutions of the first and second problems do not evolve over time and can be found by solving a static problem, whereas the third problem's optimal solution evolves over time and depends on the problem specification and the state variables. We find the dual problem of the third problem and show that the optimal reinsurance contract always has a multilayer structure. Last, we consider some examples and show that in many cases, the contract is indeed a two-layer policy.