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.

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.

scholarly journals Explicit Solutions for Survival Probabilities in the Classical Risk Model

2005 ◽  
Vol 35 (1) ◽  
pp. 113-130 ◽  
Author(s):  
Jorge M.A. Garcia
Keyword(s):  
Laplace Transform ◽  
Inversion Formula ◽  
Time Horizon ◽  
Risk Model ◽  
Explicit Solutions ◽  
Classical Risk Model ◽  
Survival Probabilities ◽  
Double Laplace Transform ◽  
Finite Time Horizon ◽  
The Classical Risk Model

The purpose of this paper is to show that, for the classical risk model, explicit expressions for survival probabilities in a finite time horizon can be obtained through the inversion of the double Laplace transform of the distribution of time to ruin. To do this, we consider Gerber and Shiu (1998) and a particular value for their penalty function. Although other methods to address the problem exist, we find this approach, perhaps, more direct and simple. For the analytic inversion, we have applied twice, after some algebra, the Laplace complex inversion formula.

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 On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 511 ◽  
Author(s):  
Wenguang Yu ◽  
Peng Guo ◽  
Qi Wang ◽  
Guofeng Guan ◽  
Qing Yang ◽  
...  
Keyword(s):  
Risk Model ◽  
Observation Interval ◽  
Claim Amount ◽  
Insurance Company ◽  
Classical Risk Model ◽  
Numerical Examples ◽  
Compound Poisson Risk Model ◽  
Capital Injection ◽  
The Classical Risk Model ◽  
Injection Function

In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.

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.

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 Explicit Solutions for Survival Probabilities in the Classical Risk Model

2005 ◽  
Vol 35 (01) ◽  
pp. 113-130 ◽  
Author(s):  
Jorge M.A. Garcia
Keyword(s):  
Laplace Transform ◽  
Inversion Formula ◽  
Time Horizon ◽  
Risk Model ◽  
Explicit Solutions ◽  
Classical Risk Model ◽  
Survival Probabilities ◽  
Double Laplace Transform ◽  
Finite Time Horizon ◽  
The Classical Risk Model

The purpose of this paper is to show that, for the classical risk model, explicit expressions for survival probabilities in a finite time horizon can be obtained through the inversion of the double Laplace transform of the distribution of time to ruin. To do this, we consider Gerber and Shiu (1998) and a particular value for their penalty function. Although other methods to address the problem exist, we find this approach, perhaps, more direct and simple. For the analytic inversion, we have applied twice, after some algebra, the Laplace complex inversion formula.

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