黑龙江大学自然科学学报
黑龍江大學自然科學學報
흑룡강대학자연과학학보
JOURNAL OF NATURAL SCIENCE OF HEILONGJIANG UNIVERSITY
2010年
2期
175-179
,共5页
Markov链%完全平衡方程%破产概率%生灭过程
Markov鏈%完全平衡方程%破產概率%生滅過程
Markov련%완전평형방정%파산개솔%생멸과정
Markov chains%full balance equation%ruin probability%birth and death process
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.
建立瞭依生滅過程賭博的風險模型,攷慮瞭賭徒單位時間要交納的費用,併假設賭徒的盈利序列為實數序列,對該模型的破產概率進行瞭研究.利用更新過程理論和馬爾可伕性質穫得瞭破產概率有關初始資本、賭博時間的兩種不同的極限形式,採用嚮後微分法給齣瞭關于條件生存概率及破產概率序列的微積分方程關繫式,得齣瞭條件破產概率的臨界情況.
건립료의생멸과정도박적풍험모형,고필료도도단위시간요교납적비용,병가설도도적영리서렬위실수서렬,대해모형적파산개솔진행료연구.이용경신과정이론화마이가부성질획득료파산개솔유관초시자본、도박시간적량충불동적겁한형식,채용향후미분법급출료관우조건생존개솔급파산개솔서렬적미적분방정관계식,득출료조건파산개솔적림계정황.
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.