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Bankruptcy theory has been the core of risk theory , the interest on the application background of its existing insurance practice , but also the probability theory . The classic insolvency theory originated in the Swedish actuary Lundberg research , but his work does not meet the strict standards of modern mathematics . Subsequently represented by Cramer Swedish School Lundberg 's work built on the basis of rigorous theory of stochastic processes , thus establishing the now recognized bankruptcy theory basic model and Theorem . With the the contemporary theoretical study of bankruptcy depth as well as actual changes in economic and financial background , innovative research model and direction of research continues to expand . Lundberg-Cramer exact representation of the model of the classic paper first introduces the independence assumption , the relative safety of the load is assumed and the adjustment coefficient is assumed , and the main results Lundberg-Cramer theorem , and then were used to certify martingale methods and update argumentation skills , both proof are now the main method to study bankruptcy problems , their introduction is conducive to our understanding of other similar results . Next, a brief introduction to the recent interest in the bankruptcy theory study , introduced on the basis of this conclusion - given in the compound binomial model , expect discounted penalty function ( φ (u) ) and Delivery push formula , as well as the initial surplus 0 , φ (0) explicit expression , which by the recurrence formula , you can find the other when the initial surplus φ (u) , u = 1, 2, 3 ... the value of the solve the model for any given initial surplus , the problem of solving the expected discounted penalty function . The article used an example to demonstrate , allows us to better understand the results . φ (u) and traditional bankruptcy probability , it is not only considering bankruptcy moment , also considering the pre-bankruptcy surplus , deficits and interest rates affect the bankruptcy , and does not require a specific form of the penalty function , and therefore powerful , such as bankruptcy probability just a special case. But it is much more than this , in fact, simply select the specific form of the penalty function , or at the same time and then choose the discount factor , you can find many classical predecessors conclusions implicit in the conclusions . Article annotation or inference , given these results .
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