On A Risk Model Under A Periodic Threshold Dividend Strategy

In this paper,we consider a risk model perturbed by diffusion under a periodic threshold dividend strategy.In order to add the randomness and adaptability of the risk model for practical problems,we research a compound Poisson model perturbed by a Brownian motion as the disturbance of premium incomes or claim sizes.At a sequence of random observation times,the insurance company makes decision on dividend payments by the fixed threshold value.Then we propose a new threshold dividend strategy: as long as the observed surplus level is larger than the maximum of the last observed surplus level(after dividend payments)and a threshold level,a fraction of the excess amount will be paid as dividends.When the observed surplus value becomes negative,the surplus process stops,which is called ruin.In this thesis,we study the Gerber-Shiu expected discounted penalty function and the expected discounted dividends under the risk model perturbed by diffusion with the periodic threshold dividend strategy.Then we derive integral equations and analytical expressions under rational Laplace transform of claim size densities.Numerical examples are also illustrated.The structures and themes of this thesis are organized as follow:Chapter 1 introduces the research background and importance of this paper,including the current research status of the classical compound Poisson model,risk model with dividend strategies as well as Gerber-Shiu function.Chapter 2 introduces some important mathematical tools in this paper: Laplace transform and Dicksom-Hipp operator.In addition,it also introduces the risk model perturbed with diffusion under the periodic threshold dividend strategy and discounted density in this paper.Chapter 3 and Chapter 4 research the Gerber-Shiu expected discounted penalty function and the expected discounted dividend payments of this risk model.Then we derive the integral equation as well as explicit results.Chapter 5 presents some numerical results of the research results with description as well as analysis under the given parameter values and rational claim size densities.Then we can get some properties of the research results.