赌徒破产概率的生灭过程模型

建立了依生灭过程赌博的风险模型,考虑了赌徒单位时间要交纳的费用,并假设赌徒的盈利序列为实数序列,对该模型的破产概率进行了研究。利用更新过程理论和马尔可夫性质获得了破产概率有关初始资本、赌博时间的两种不同的极限形式,采用向后微分法给出了关于条件生存概率及破产概率序列的微积分方程关系式,得出了条件破产概率的临界情况。

Birth and death process model on ruin probability of gamblers

A birth and death process model on ruin probability of gamblers is developed. The costs of gamblers per unit time are considered. It is assumed that the profit sequence is the real number sequence. The ruin probability of the model is mainly studied. Two different limit forms about initial capital and playing time are derived by using a renewal process theory and Markov property. Furthermore, the differential and integral equations are given, which is satisfied by the conditional survive probability and the ruin probability, and then critical situations of the condi-tional ruin probability are gotten.