scholarly journals Does Markov-Modulation Increase the Risk?

1995 ◽  
Vol 25 (1) ◽  
pp. 49-66 ◽  
Author(s):  
Søren Asmussen ◽  
Andreas Frey ◽  
Tomasz Rolski ◽  
Volker Schmidt
Keyword(s):  
Arrival Rate ◽  
Poisson Model ◽  
Stochastic Ordering ◽  
Claim Size ◽  
Compound Poisson ◽  
Compound Poisson Model ◽  
Markov Modulated ◽  
Stop Loss ◽  
Risk Processes ◽  
Over Time

AbstractIn this paper we compare ruin functions for two risk processes with respect to stochastic ordering, stop-loss ordering and ordering of adjustment coefficients. The risk processes are as follows: in the Markov-modulated environment and the associated averaged compound Poisson model. In the latter case the arrival rate is obtained by averaging over time the arrival rate in the Markov modulated model and the distribution of the claim size is obtained by averaging the ones over consecutive claim sizes.

On a Dual Model with Multi-Layer Dividend Strategy under Stochastic Interest

2011 ◽  
Vol 422 ◽  
pp. 775-778
Author(s):  
Jin Sheng Yin
Keyword(s):  
Differential Equations ◽  
Poisson Model ◽  
Dual Model ◽  
Exponential Distributions ◽  
Compound Poisson ◽  
Compound Poisson Model ◽  
Surplus Process ◽  
Stochastic Interest ◽  
Aggregate Claims

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual model of the compound Poisson model with multi-layer dividend strategy under stochastic interest. We derive a set of integro-differential equations satisfied by the expected total discounted dividends until ruin. The cases where profits follow an exponential distributions are solved.

scholarly journals The finite-time ruin probability of the compound Poisson model with constant interest force

2005 ◽  
Vol 42 (03) ◽  
pp. 608-619 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Poisson Model ◽  
Compound Poisson ◽  
Finite Time Ruin Probability ◽  
Compound Poisson Model ◽  
Interest Force ◽  
Constant Interest Force ◽  
Claim Size Distribution ◽  
Constant Interest

In this paper, we establish a simple asymptotic formula for the finite-time ruin probability of the compound Poisson model with constant interest force and subexponential claims in the case that the initial surplus is large. The formula is consistent with known results for the ultimate ruin probability and, in particular, is uniform for all time horizons when the claim size distribution is regularly varying tailed.

scholarly journals On the Distribution of the Surplus Prior and at Ruin

1999 ◽  
Vol 29 (2) ◽  
pp. 227-244 ◽  
Author(s):  
Hanspeter Schmidli
Keyword(s):  
Asymptotic Behaviour ◽  
Ruin Probability ◽  
Poisson Model ◽  
Subexponential Distributions ◽  
Compound Poisson ◽  
Initial Capital ◽  
Compound Poisson Model ◽  
Explicit Expressions

AbstractConsider 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 case of subexponential distributions and some intermediate cases are discussed.

scholarly journals Error Bounds for Compound Poisson Approximations of the Individual Risk Model

1992 ◽  
Vol 22 (2) ◽  
pp. 135-148 ◽  
Author(s):  
Nelson De Pril ◽  
Jan Dhaene
Keyword(s):  
Risk Model ◽  
General Setting ◽  
Poisson Model ◽  
Individual Risk ◽  
Compound Poisson ◽  
Aggregate Claims ◽  
The Individual ◽  
Stop Loss ◽  
Work Done

AbstractThe approximation of the individual risk model by a compound Poisson model plays an important role in computational risk theory. It is thus desirable to have sharp lower and upper bounds for the error resulting from this approximation if the aggregate claims distribution, related probabilities or stop-loss premiums are calculated.The aim of this paper is to unify the ideas and to extend to a more general setting the work done in this connection by Bühlmann et al. (1977), Gerber (1984) and others. The quality of the presented bounds is discussed and a comparison with the results of Hipp (1985) and Hipp & Michel (1990) is made.

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