The Study Of Risk Model With Dividend Strategy

Risk theory is the core content of Actuarial Science. People who work in the field of economics and insurance pay more and more atten-tion to it. The dividend strategies in insurance risk model has become one of the hot topics in the current research. The thesis discusses sev-eral dividend risk model based on classic risk model, we obtained some results, the main ideas of the thesis are as follows:In the first chapter, the history and current development of risk theory are briefly reviewed. Furthermore, we make an outline of the main research work of this thesis.In Chapter2, elementary basis of knowledge is presented briefly.In Chapter3, a diffusion perturbed classic compound Poisson risk model in the presence of a linear dividend barrier is considered. Par-tial integro-differential equations for the moment generating function and the nth moment of the present value of all dividends until ruin are derived. Moreover, explicit solutions for the nth moment of the present value of dividend payments are obtained when the individual claim size distribution is exponential. We also provided some numer-ical examples to illustrate the applications of the explicit solutions. Finally we derive partial integro-differential equations with boundary conditions for the Gerber-Shiu function.Chapter4studies a dual risk model with linear dividend barrier, the integro-differential equations for the survival probability is ob-tained. Furthermore, we obtain the explicit expression of the survival probability for exponential claim. Finally, the explicit expression of survival probability in the dual risk process with Brownian motion is obtained.In Chapter5, we consider the dual of the compound Poisson risk model with random observation time and constant dividend barrier strategy. The integro-differential equations for the expected total dis-counted dividend payments and ruin probability are derived. More-over, explicit solutions for the ruin probability and the expected total discounted dividend payments are obtained when the profits follows an exponential distribution. Numerical illustrations for the effect of several sets of parameters and random observation time on the per-formance of the dividend strategy are given.In Chapter6, we consider the Markov-modulated dual risk model with diffusion and constant dividend barrier, the integro-differential equations for the expected total discounted dividend payments are ob-tained. Moreover, in the two-state model, explicit results are obtained when both claim amounts are exponentially distributed and mixed ex-ponentially distributed. Finally, we give some numerical examples.In Chapter7, we consider the Markov arrival risk model with tax payments. Systems of integro-differential equations satisfied by the ex-pected discounted tax payments and the non-ruin probability in terms of the ruin probabilities under the Markov arrival risk model without tax are established. The analytical solutions of the systems of integro-differential equations are also obtained by the iteration method.In Chapter8, we give a brief summary of the thesis and intro-duction to future work.