The Distribution of the Time of Ruin, the Surplus Immediately before Ruin and Deficit at Ruin under Two Sided Risk Renewal Process
نویسندگان
چکیده
منابع مشابه
The moments of the time of ruin , the surplus before ruin , and the deficit at ruin
In this paper we extend the results in Lin and Willmot (1999 Insurance: Mathematics and Economics 25, 63–84) to properties related to the joint and marginal moments of the time of ruin, the surplus before the time of ruin, and the deficit at the time of ruin. We use an approach developed in Lin and Willmot (1999), under which the solution to a defective renewal equation is expressed in terms of...
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This paper presents an explicit characterization for the joint probability density function of the surplus immediately prior to ruin and the deficit at ruin for a general risk process, which includes the Sparre-Andersen risk model with phase-type inter-claim times and claim sizes. The model can also accommodate a Markovian arrival process which enables claim sizes to be correlated with the inte...
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This paper investigates the moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. Using the integro-differential equation that we establish, we obtain some explicit expressions for the moments. Furthermore, when the claim size is exponentially and subexponentially distributed, asymptotic relationships for the moments are derived as the initial capital tends t...
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Properties of the distribution of the deficit at ruin in the stationary renewal risk model are studied. A mixture representation for the conditional distribution of the deficit at ruin (given that ruin occurs) is derived, as well as a stochastic decomposition involving the residual lifetime associated with the maximal aggregate loss. In the case where the individual claims have a phase-type dis...
متن کاملOn the Distribution of the Surplus Prior and at Ruin
Consider a classical compound Poisson model. The safety loading can be positive, negative or zero. Explicit expressions for the distributions of the surplus prior and at ruin are given in terms of the ruin probability. Moreover, the asymptotic behaviour of these distributions as the initial capital tends to infinity are obtained. In particular, for positive safety loading the Cramer case, the c...
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ژورنال
عنوان ژورنال: Journal of Mathematical Finance
سال: 2017
ISSN: 2162-2434,2162-2442
DOI: 10.4236/jmf.2017.73032