Stochastic Bankruptcy Problem In The Generalized Erlang(n) Risk Model

In the classical risk theory, the definition of ruin is well known. But, the definition of ruin is not practical. So, some authors consider a relaxed ruin definition that is bankrupt-cy. In this case, the insurer can continue to operate despite the insurer has negative surplus. In this paper, we study the bankruptcy probabilities for a generalized Erlang(n)risk process.In this paper, we model the surplus of insurer by R(t), the distribution of interclaim times is the generalized Erlang(n) distribution. Because it can be denoted by a sum of n independent, exponentially distributed random variables, this will allow to use Markovian arguments due to the lack-of-memory property of the exponential distribution. In this way, we can see the interclaim times of the surplus R(t) as special interclaini times that include n jumps; which interclaim times have a exponential distribution. But, the size of the i-th jump (i=1, 2, · · · , n -1) is zero; the last(the n-th) is the real claim.In this paper, the structure is as follows:In chapter 1, we give the definition of bankruptcy and the background and meaning,and we define the risk model that we want to study;In chapter 2, we derive an integro-differential equation for ?(x); when n=2, ?1=?2 =?, we obtain exact expression for ?(x) with constant bankruptcy rate function. On other hand, we obtain the approximated expression for ?(x) with general bankruptcy rate function.In chapter 3, we discuss the discounted penalty function in the definition of bankrupt-cy and derive the integro-differential equation for it. And we discuss the special case when n = 2.In chapter 4, we give the numerical illustration in detail.