Several Types Of Boundary Threshold Dividend Strategy Gerber-Shiu Discounted Penalty Function Study

Ruin theory means that insurers have some initial premise of the assets, after a period of operation, Surplus for the first time into a negative situation, only a mathematical concept, this failure does not necessarily mean the insurance company ruin. In modern Ruin theory, three important indicators of general concern are:the time of Ruin, the deficit at ruin, the surplus immediately before the time of ruin.Hans U. Gerber and EliasS.W.Shiu constructed the famous expected dis-counted penalty function, also called Gerber-Shiu discounted penalty function. The instantaneous profit function is the deficit at ruin and the surplus immediately prior to ruin two indicators, Very convenient to describe the probability of Ruin, ruin events prior to the insolvency of the Laplace transform as well as the deficit at ruin and the surplus immediately prior to ruin between the joint density function.Insurance risk model in the initial dividend strategy proposed by the De Finetti, more realistic response to an insurance portfolio cash flow. After two kinds of dividend strategy attracted our attention:one is the constant value Dividend risk model is also known as total dividend model, when the surplus under a constant value, no dividends to shareholders or the insurant, However, once surplus above this boundary, all the surplus over all as a dividend to shareholders, Gerber initial study of this strategy. The other is the threshold dividend strategy, the provisions of this risk model, when the surplus above the boundary, then the dividend less than the premium income to shareholders or policyholders part of this strategy first Gerber, Buhlmann presented, followed by the boundary and depends on the time constant of the linear boundary, many scholars made a lot of work. This dividend strategy and the introduction of the two classical risk model, while the introduction of dependent risks and the classical risk model with a disturbance, and then draw the relevant conclusions of the two dividend strategy to promote, first introduced under the threshold constant Dividend dividend strategy, given the model Gerber-Shiu discounted penalty function, the linear Dividend Barrier is given under the Gerber-Shiu discounted penalty function results; the introduction of linear Dividend Barrier and dependent under the threshold dividend strategy risk model is given to satisfy these two situation Gerber-Shiu discounted penalty function; the introduction of the risk model perturbed obtained the probability of survival under such circumstances, the present value of expected dividend payments, Gerber-Shiu discounted penalty function and other results.