Reinsurance and Dividend Control with Fixed Costs and Regime Switching

Summary

This paper formulates an insurer’s joint reinsurance and dividend decisions as a stochastic control problem. The risk process is Brownian, with drift and volatility changing through endogenous regime switching. Dividend payments incur fixed transaction costs, and the objective is to maximize expected discounted dividends net of those costs until the insurer’s reserves are ruined.

The authors prove that the value function is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with a nonlocal operator. For almost all parameter configurations, they characterize an optimal policy: dividends follow a two-barrier impulse rule, while the reinsurance proportion is specified in feedback form. Numerical examples illustrate the theoretical results, but the document provides no reported numerical performance measures or empirical validation. The findings concern an insurance risk model, so their direct relevance to trading is limited; the control methods and treatment of fixed costs may still interest quantitative researchers studying related decision problems.

Key ideas

• The model jointly optimizes proportional reinsurance and dividend payments under regime switching.
• Fixed transaction costs make dividend payments an impulse-control decision.
• The value function is characterized as the unique viscosity solution of an HJB equation with a nonlocal operator.
• The dividend policy uses two barriers, while reinsurance is selected through a feedback rule.
• Numerical examples illustrate the results, which are specific to the stated insurance model.

Tags

# 2609.32686


# Optimal Reinsurance-Dividend Strategy with Fixed Transaction Costs in a Regime-Switching Brownian Risk Model: A Viscosity Solution to the Impulse Control Problem









We consider a problem of optimal proportional reinsurance-dividend distribution under a Brownian risk model, where both the drift and volatility coefficients are subject to endogenous regime-switching. Dividend payments are subject to fixed transaction costs. The problem is formulated as a two-dimensional stochastic control problem, and we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation with nonlocal operator. For almost all parameter configurations, we explicitly characterize the optimal strategy that maximizes the expected total discounted dividends net of transaction costs until ruin. The optimal dividend policy is a two-barrier impulsive strategy, while the optimal reinsurance proportion is given in feedback form. Numerical examples are provided to illustrate the optimality results.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.