scholarly journals The Density of the Time to Ruin in the Classical Poisson Risk Model

2005 ◽  
Vol 35 (01) ◽  
pp. 45-60 ◽  
Author(s):  
David C.M. Dickson ◽  
Gordon E. Willmot
Keyword(s):  
Laplace Transform ◽  
Finite Time ◽  
Risk Model ◽  
Erlang Distribution ◽  
Claim Amount ◽  
Ruin Probabilities ◽  
Classical Risk Model ◽  
The Individual ◽  
The Classical Risk Model ◽  
Poisson Risk Model

We derive an expression for the density of the time to ruin in the classical risk model by inverting its Laplace transform. We then apply the result when the individual claim amount distribution is a mixed Erlang distribution, and show how finite time ruin probabilities can be calculated in this case.

scholarly journals The Density of the Time to Ruin in the Classical Poisson Risk Model

2005 ◽  
Vol 35 (1) ◽  
pp. 45-60 ◽  
Author(s):  
David C.M. Dickson ◽  
Gordon E. Willmot
Keyword(s):  
Laplace Transform ◽  
Finite Time ◽  
Risk Model ◽  
Erlang Distribution ◽  
Claim Amount ◽  
Ruin Probabilities ◽  
Classical Risk Model ◽  
The Individual ◽  
The Classical Risk Model ◽  
Poisson Risk Model

We derive an expression for the density of the time to ruin in the classical risk model by inverting its Laplace transform. We then apply the result when the individual claim amount distribution is a mixed Erlang distribution, and show how finite time ruin probabilities can be calculated in this case.

scholarly journals On the Ruin Probability Under a Class of Risk Processes

2002 ◽  
Vol 32 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Wang Rongming ◽  
Liu Haifeng
Keyword(s):  
Laplace Transform ◽  
Renewal Process ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Claim Amount ◽  
Classical Risk Model ◽  
Finite Time Ruin Probability ◽  
Risk Processes ◽  
The Classical Risk Model

AbstractIn this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the finite time ruin probability is well given when the claim amount distribution is a mixed exponential. As its consequence, a well-known result about ultimate ruin probability in the classical risk model is obtained.

Some Finite Time Ruin Problems

2007 ◽  
Vol 2 (2) ◽  
pp. 217-232 ◽  
Author(s):  
D. C. M. Dickson
Keyword(s):  
Finite Time ◽  
Risk Model ◽  
Claim Amount ◽  
Density Functions ◽  
Classical Risk Model ◽  
Deficit At Ruin ◽  
The Deficit At Ruin ◽  
Aggregate Claims ◽  
The Individual ◽  
The Classical Risk Model

ABSTRACTIn the classical risk model, we use probabilistic arguments to write down expressions in terms of the density function of aggregate claims for joint density functions involving the time to ruin, the deficit at ruin and the surplus prior to ruin. We give some applications of these formulae in the cases when the individual claim amount distribution is exponential and Erlang(2).

scholarly journals The Distribution of the time to Ruin in the Classical Risk Model

2002 ◽  
Vol 32 (2) ◽  
pp. 299-313 ◽  
Author(s):  
David C.M. Dickson ◽  
Howard R. Waters
Keyword(s):  
Finite Time ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Classical Risk Model ◽  
The Classical Risk Model

AbstractWe study the distribution of the time to ruin in the classical risk model. We consider some methods of calculating this distribution, in particular by using algorithms to calculate finite time ruin probabilities. We also discuss calculation of the moments of this distribution.

scholarly journals Recursive Calculation of Survival Probabilities

1991 ◽  
Vol 21 (2) ◽  
pp. 199-221 ◽  
Author(s):  
David C. M. Dickson ◽  
Howard R. Waters
Keyword(s):  
Finite Time ◽  
Approximate Calculation ◽  
Risk Model ◽  
Classical Risk Model ◽  
Infinite Time ◽  
Numerical Examples ◽  
Survival Probabilities ◽  
Recursive Calculation ◽  
The Stability ◽  
The Classical Risk Model

AbstractIn this paper we present an algorithm for the approximate calculation of finite time survival probabilities for the classical risk model. We also show how this algorithm can be applied to the calculation of infinite time survival probabilities. Numerical examples are given and the stability of the algorithms is discussed.

scholarly journals On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Huiming Zhu ◽  
Ya Huang ◽  
Xiangqun Yang ◽  
Jieming Zhou
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Claim Amount ◽  
Classical Risk Model ◽  
Main Claim ◽  
Expected Discounted Penalty Function ◽  
The Laplace Transform ◽  
Discounted Penalty Function ◽  
The Classical Risk Model ◽  
Expected Discounted Penalty

We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function.

On Numerical Evaluation of Finite Time Survival Probabilities

1999 ◽  
Vol 5 (3) ◽  
pp. 575-584 ◽  
Author(s):  
D.C.M. Dickson
Keyword(s):  
Finite Time ◽  
Numerical Evaluation ◽  
Risk Model ◽  
Classical Risk Model ◽  
Probability Of Ruin ◽  
Survival Probabilities ◽  
Computational Aspects ◽  
The Classical Risk Model

ABSTRACTIn this paper we review three algorithms to calculate the probability of ruin/survival in finite time for the classical risk model. We discuss the computational aspects of these algorithms and consider the question of which algorithm should be preferred.

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