Optimal dividend and reinsurance strategies with financing and liquidation value

This study investigates a combined optimal financing, reinsurance and dividend distribution problem for a big insurance portfolio. A manager can control the surplus by buying proportional reinsurance, paying dividends and raising money dynamically. The transaction costs and liquidation values at bankruptcy are included in the risk model. Under the objective of maximising the insurance company's value, we identify the insurer's joint optimal strategies using stochastic control methods. The results reveal that managers should consider financing if and only if the terminal value and the transaction costs are not too high, less reinsurance is bought when the surplus increases or dividends are always distributed using the barrier strategy.postprin

Optimal reinsurance and dividend for a diffusion model with capital injection: variance premium principle

This paper considers the optimal dividend problem with proportional reinsurance and capital injection for a large insurance portfolio. In particular, the reinsurance premium is assumed to be calculated via the variance principle instead of the expected value principle. Our objective is to maximize the expectation of the discounted dividend payments minus the discounted costs of capital injection. This optimization problem is studied in four cases depending on whether capital injection is allowed and whether there exist restrictions on dividend policies. In all cases, closed-form expressions for the value function and optimal dividend and reinsurance policies are obtained. From the results, we see that the optimal dividend distribution policy is of threshold type with a constant barrier, and that the optimal ceded proportion of risk exponentially decreases with the initial surplus and remains constant when the initial surplus exceeds the dividend barrier. Furthermore, we show that the optimization problem without capital injection is the limiting case of the one with capital injection when the proportional transaction cost goes to infinity. © 2011 Elsevier B.V.postprin

Reinsurance and dividend management

Includes bibliographical references.In this dissertation we set to find the dual optimal policy of a dividend payout scheme for shareholders with a risk-averse utility function and the retention level of received premiums for an insurance company with the option of reinsurance. We set the problem as a stochastic control problem. We then solve the resulting second-order partial differential equation known as Hamilton-Jacobi-Bellman equation. We find out that the optimal retention level is linear with the current reserve up to a point whereupon it is optimal for the insurance company to retain all business. As for the optimal dividend payout scheme, we find out that it is optimal for the company not to declare dividends and we make further explorations of this result

Dynamic optimal reinsurance and dividend-payout in finite time horizon

This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurer in a finite time horizon. The goal of the insurer is to maximize its expected cumulative discounted dividend payouts until bankruptcy or maturity which comes earlier. The insurer is allowed to dynamically choose reinsurance contracts over the whole time horizon. This is a mixed singular-classical control problem and the corresponding Hamilton-Jacobi-Bellman equation is a variational inequality with fully nonlinear operator and with gradient constraint. The $C^{2,1}$ smoothness of the value function and a comparison principle for its gradient function are established by penalty approximation method. We find that the surplus-time space can be divided into three non-overlapping regions by a risk-magnitude-and-time-dependent reinsurance barrier and a time-dependent dividend-payout barrier. The insurer should be exposed to higher risk as surplus increases; exposed to all the risks once surplus upward crosses the reinsurance barrier; and pay out all reserves in excess of the dividend-payout barrier. The localities of these regions are explicitly estimated.Comment: 7 figure

Optimal control of risk process in a regime-switching environment

This paper is concerned with cost optimization of an insurance company. The surplus of the insurance company is modeled by a controlled regime switching diffusion, where the regime switching mechanism provides the fluctuations of the random environment. The goal is to find an optimal control that minimizes the total cost up to a stochastic exit time. A weaker sufficient condition than that of (Fleming and Soner 2006, Section V.2) for the continuity of the value function is obtained. Further, the value function is shown to be a viscosity solution of a Hamilton-Jacobian-Bellman equation.Comment: Keywords: Regime switching diffusion, continuity of the value function, exit time control, viscosity solutio