ruin probability
1.RUIN PROBABILITY FOR DOUBLE COMPOUND POISSON PROCESS WITH BONUS LINE
4.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.
5.A double-type-insurance risk model with constant interest is introduced. Meanwhile, the explicit expression for the ruin probability Ψ(0), the Cramér-Lundberg approximation for the ruin probability Ψ(u), the explicit expression for Ψ(u) and its Lundberg upper bound are given.
6.Theorem 4.1 On the basic assumption of the model, for the ruin probability will satisfywhere Theorem 5.1 Let , for , then.
7.It is shown that the ultimate survival probability (or the ultimate ruin probability) satisfies certain defective renewal equation, and then its Cramér-Lundberg asymptotic property is investigated by using the standard techniques of renewal theory.
8.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.
9.We also consider local limit theorems for ruin probability in the classical risk model perturbed by diffusion and the Erlang(n, β) risk model.
10.As a special case, we deliver a concrete asymptotic formula for local ruin probability in the multi-delayed Erlang (n, A) risk model.
