Abstract
The first method, essentially due to GOOVAERTS and DE VYLDER, uses the connection between the probability of ruin and the maximal aggregate loss random variable, and the fact that the latter has a compound geometric distribution. For the second method, the claim amount distribution is supposed to be a combination of exponential or translated exponential distributions. Then the probability of ruin can be calculated in a transparent fashion; the main problem is to determine the nontrivial roots of the equation that defines the adjustment coefficient. For the third method one observes that the probability of ruin is related to the stationary distribution of a certain associated process. Thus it can be determined by a single simulation of the latter. For the second and third methods the assumption of only proper (positive) claims is not needed
KEYWORDS probability of ruin, combination of exponentials, simulation.
Volume
19:1
Page
71-90
Year
1994
Categories
Financial and Statistical Methods
Risk Pricing and Risk Evaluation Models
Capital Theory
Financial and Statistical Methods
Aggregation Methods
Collective Risk Model
Financial and Statistical Methods
Risk Pricing and Risk Evaluation Models
Probability of Ruin
Financial and Statistical Methods
Loss Distributions
Severity
Financial and Statistical Methods
Simulation
Publications
ASTIN Bulletin
