ﻻ يوجد ملخص باللغة العربية
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.
In this paper we propose and solve an optimal dividend problem with capital injections over a finite time horizon. The surplus dynamics obeys a linearly controlled drifted Brownian motion that is reflected at the origin, dividends give rise to time-d
Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash-flows are discounted at a stochastic dynamic rate. Dividends can be paid
We consider an optimal control problem of a property insurance company with proportional reinsurance strategy. The insurance business brings in catastrophe risk, such as earthquake and flood. The catastrophe risk could be partly reduced by reinsuranc
We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize her expec
This paper considers nonlinear regular-singular stochastic optimal control of large insurance company. The company controls the reinsurance rate and dividend payout process to maximize the expected present value of the dividend pay-outs until the tim