probability of ruin
2.In chapter one, we introduce the Erlang(2) risk process with constant interest force and give the definition of the probability of ruin, the surplus immediately before ruin, the deficit at ruin, the joint distribution of the surplus immediately before ruin and the deficit at ruin, the expected discounted penalty at ruin respectively.
4.Sparre Andersen considered the situation in which claims occur as a general renewal process in 1957, then he constructed the renewal risk model and began to study ruin probability. Since then, the calculation of ruin probability became increasingly important. See, [2] [3] [4] [15] for details.
5.In this paper,we discuss a compound renewal risk model with premium arrival by equilibrium renewal process,then we get the live probability in finite time t,the joint distribution of the time of ruin T and the asset surplus U(T) at ruin,and the joint distribution of the time of ruin T and the surplus immediately before ruin U(T ).
7.On the condition that police arrival and insurance indemnity follow Cox process,we establish a double Cox risk model with additional premium and obtain the upper bound of ruin probability. Furthermore,under the assumption that police arrival and insurance indemnity follow process with the same accumulate intension,we provide an explicit expression of the ruin probability formula.
8.On the assumption that the claims size belongs to the heavy-tailed class, we get a desired tail-equivalence relationship of ruin probability, which is surprisingly in accordance with that proved in classical Cramér-Lundberg model.
9.Sparre Andersen (1957) considered the situation in which claims occur as a general renewal process, and an explicit result for the ultimate ruin probability was derived for a particular case. The explicit expression for Laplace transform of the ruin time with exponentially claim amount distribution is obtained by Malinovskii (1998); and Wang and Liu (2002) generalized the result to the case when claim amount has the mixed distribution of two exponentials.
10.This dissertion mainly study the Erlang(2) risk model with constant interest force, we consider some important distributions and rusults: the non-ruin probability, the surplus immediately before ruin, the deficit at ruin, the joint distribution of the surplus immediately before ruin and the deficit at ruin, the expected discounted penalty at ruin and so on.
