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 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 Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times

2004 ◽  
Vol 34 (2) ◽  
pp. 315-332 ◽  
Author(s):  
F. Avram ◽  
M. Usábel
Keyword(s):  
Laplace Transform ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Theoretical Point ◽  
Finite Time Ruin Probability ◽  
Double Laplace Transform ◽  
Phase Type ◽  
Interarrival Times ◽  
Renewal Risk

This paper shows how the multivariate finite time ruin probability function, in a phase-type environment, inherits the phase-type structure and can be efficiently approximated with only one Laplace transform inversion.From a theoretical point of view, we also provide below a generalization of Thorin’s formula (1971) for the double Laplace transform of the finite time ruin probability, by considering also the deficit at ruin; the model is that of a Sparre Andersen (renewal) risk process with phase-type interarrival times.In the case when the claims distribution is of phase-type as well, we obtain also an alternative formula for the single Laplace transform in time (or “exponentially killed probability’’), in terms of the roots with positive real part of the Lundberg’s equations, which complements Asmussen’s representation (1992) in terms of the roots with negative real part.

scholarly journals Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times

2004 ◽  
Vol 34 (02) ◽  
pp. 315-332 ◽  
Author(s):  
F. Avram ◽  
M. Usábel
Keyword(s):  
Laplace Transform ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Theoretical Point ◽  
Finite Time Ruin Probability ◽  
Double Laplace Transform ◽  
Phase Type ◽  
Interarrival Times ◽  
Renewal Risk

This paper shows how the multivariate finite time ruin probability function, in a phase-type environment, inherits the phase-type structure and can be efficiently approximated with only one Laplace transform inversion. From a theoretical point of view, we also provide below a generalization of Thorin’s formula (1971) for the double Laplace transform of the finite time ruin probability, by considering also the deficit at ruin; the model is that of a Sparre Andersen (renewal) risk process with phase-type interarrival times. In the case when the claims distribution is of phase-type as well, we obtain also an alternative formula for the single Laplace transform in time (or “exponentially killed probability’’), in terms of the roots with positive real part of the Lundberg’s equations, which complements Asmussen’s representation (1992) in terms of the roots with negative real part.

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).

The finite time ruin probability in a risk model with capital injections

2013 ◽  
Vol 2015 (4) ◽  
pp. 301-318 ◽  
Author(s):  
Ciyu Nie ◽  
David C.M. Dickson ◽  
Shuanming Li
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Finite Time Ruin Probability ◽  
Capital Injections

The finite-time ruin probability of a risk model with stochastic return and Brownian perturbation

2018 ◽  
Vol 35 (3) ◽  
pp. 1173-1189 ◽  
Author(s):  
Kaiyong Wang ◽  
Lamei Chen ◽  
Yang Yang ◽  
Miaomiao Gao
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Finite Time Ruin Probability
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