The Fruther Research On Ruin Problem Model Of Gamblers

The ruin problem of gamblers is a classic problem. In the field of foreign actuarial science has a certain extent achievement. With the diverse ways of life, gambling has gradually concerned by the academic circles. The size of the ruin probability is directly related to the vital interests of gamers, The size of the ruin probability is directly related to the vital interests of gamers, and declares limits of game to them, therefore it makes people much better understand gambling.In this paper, we considered asymmetric gambler's ruin problem from the traditional discrete model, and the initial fortune of players is special monotone increasing natural number sequence, popularize the gambler risk theory of application. And then, another new model is developed, which is called a birth and death process model on ruin probability of gamblers. The costs of gamblers at per unit time are considered and profit sequence is the real number sequence, two different limit forms are derived by using a renewal process theory and Markov property. Furthermore, the integral equation system is given, and then critical situations of the conditional ruin probability are gotten.There are five chapters. The research background and development history of the risk theory are summarized in the first chapter, then the negative risk theory and gambler ruin problem in the present research are introduced.The second chapter summarized the main basic knowledge which are used in the paper, including foundations of probability theory, risk theory, stochastic process and stopping theorem. This chapter laid a good foundation for the follo- wing chapters.In the third chapter, we considered asymmetric gambler's ruin problem with n players. And a detailed profile is made as to the same initial capital sit- uation, and corresponding results are got under the symmetric game.In the fourth chapter, we researched the asymmetric gambler's ruin proble- m, in which the initial fortune of players is simple monotone increasing natural number sequence. Under the circumstances, the expected ruin time and the pro- babilities of ruin are given.In the paper, another new model is developed, which is called a birth and death process model on ruin probability of gamblers, the ruin probability of the model is mainly studied.