Random Bankruptcy Of Risk Models Under Markov Environment

In risk theory,the Markov-Modulated risk model is one of the important risk processes.And ruin theory is an important part of insurance theory.Therefore,to study the problems of Markov-Modulated risk model plays an important role in insurance and finance.In the classical risk theory,when the surplus becomes negative firstly,the ruin is claimed.Recently,many scholars have considered a generalized concept of ruin,random bankruptcy.It assumes that when the surplus becomes negative the company can continue to operate in a certain circumstances.That is to say,the ruin probability relates to a function which is about the negative surplus.The function is called bankrupt rate function.In this paper,we study the probability of ultimate bankruptcy under this case.Many scholars have studied the random bankruptcy of the classical risk model.For example,Albrecher(2011)extended the concept of ruin to random bankruptcy;Albrecher and Lautscham(2013)proposed the concept of the bankruptcy rate and studied the probability of failure probability under the Erlang(n)risk model.For more results,we refer to:Snoussi(2002),Li and Lu(2005),Cheung and Landriaclt(2009),Asmussen(2011)etc.In this paper,we study the problem of random bankruptcy of Markov-Modulated risk processes with the bankrupt rate function.This paper is organized as follows.In the first chapter,we introduce the Markov-Modulated risk process and give some related definitions and properties of random bankruptcy which are used in this paper;In the second chapter,we give the expressions of ?r(u)and ?l(u)of the random prob-ability of ruin at the ruin time for the Markov-Modulated risk model under the constant premium rate with ruin rate function and show a special case;In the last chapter,we investigate the expressions of ?r(u)and?l(u)of the Markov-Modulated risk model with ruin rate function at the dynamic premium rate.