Monte-Carlo estimate of the probability of ruin in a compound poisson model of risk theory

Consider the classical compound Poisson model of risk theory, in which dividends are paid to the shareholders according to a barrier strategy. Let b* be the level of the barrier that maximizes the expectation of the discounted dividends until ruin. This paper is inspired by Dickson and Waters (2004). They point out that the shareholders should be liable to cover the deficit at ruin. Thus, they consider b0 , the level of the barrier that maximizes the expectation of the difference between the discounted dividends until ruin and the discounted deficit at ruin. In this paper, b* and b0 are compared, when the claim amount distribution is exponential or a combination of exponentials.

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Maximizing Dividends without Bankruptcy

Astin Bulletin ◽

10.1017/s0515036100014392 ◽

2006 ◽

Vol 36 (1) ◽

pp. 5-23 ◽

Cited By ~ 17

Author(s):

Hans U. Gerber ◽

Elias S.W. Shiu ◽

Nathaniel Smith

Keyword(s):

Poisson Model ◽

Risk Theory ◽

Claim Amount ◽

Barrier Strategy ◽

Deficit At Ruin ◽

Compound Poisson ◽

Compound Poisson Model ◽

The Deficit At Ruin ◽

The Difference

Consider the classical compound Poisson model of risk theory, in which dividends are paid to the shareholders according to a barrier strategy. Let b* be the level of the barrier that maximizes the expectation of the discounted dividends until ruin. This paper is inspired by Dickson and Waters (2004). They point out that the shareholders should be liable to cover the deficit at ruin. Thus, they consider b0, the level of the barrier that maximizes the expectation of the difference between the discounted dividends until ruin and the discounted deficit at ruin. In this paper, b* and b0 are compared, when the claim amount distribution is exponential or a combination of exponentials.

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A Generalized Compound Poisson Model for Consumer Purchase Panel Data Analysis

Journal of the American Statistical Association ◽

10.1080/01621459.1978.10480081 ◽

1978 ◽

Vol 73 (364) ◽

pp. 706-713 ◽

Cited By ~ 8

Author(s):

Allan E. Paull

Keyword(s):

Data Analysis ◽

Panel Data ◽

Panel Data Analysis ◽

Poisson Model ◽

Compound Poisson ◽

Compound Poisson Model

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Bias of the Monte-Carlo estimate of keff for a nuclear reactor calculated by generation method with a constant number of points

Journal of Soviet Mathematics ◽

10.1007/bf01097348 ◽

1992 ◽

Vol 61 (5) ◽

pp. 2374-2382

Author(s):

R. Kh. Khairullin

Keyword(s):

Monte Carlo ◽

Nuclear Reactor ◽

Constant Number ◽

Monte Carlo Estimate ◽

Carlo Estimate

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.422.775 ◽

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.

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