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Showing 6 results for Ruin Probability
Abouzar Bazyari,
Volume 6, Issue 1 (8-2012)
Abstract
In the individual risk processes of an insurance company with dependent claim sizes, determination of the ruin probability and time to ruin are very important. Exact computing of theses probabilities, because of it's complex structure, is not easy. In this paper, Monte Carlo simulation method is used to obtain the ruin probabilities estimates, times to ruin and confidence interval for the ruin probability estimates of the mentioned process for different dependence level of claims. In this simulation the multivariate Frank copula function and Marshall and Olkin's algorithm are provided to generate the dependent claims. Then it has shown that with increasing the dependence level of claim sizes the ruin probability of the risk process increases, while its time to ruin decreases
Abouzar Bazyari,
Volume 11, Issue 1 (9-2017)
Abstract
The collective risk model of insurance company with constant initial capital when process of claims number have the poisson distribution with constant rate is considered. For computing the infinite time ruin probability the stochastic processes and differential equations are used. Also a formula is obtained to compute the Lundberg approximation in finding the approximate of infinite time ruin probability based on the distribution function of claims number. The numerical examples to illustrate these results are given and showed that for any value of initial capital the approximate of our infinite time ruin probability is closer to its real value rather than the ruin probability computed by other authors and has less error.
Zahra Ranginian, Maede Behfrouz, Abouzar Bazyari,
Volume 12, Issue 2 (3-2019)
Abstract
In this paper, it is shown that using the cliams with Pareto distribution for computing the ruin probabilities could has detriment for the heads of insurance company. With computing the relative error of these cliams it is shown that the estimation of claims mean is not suitable in insurance models. We will show that existance of claims with Pareto distribution in the excess of loss reinsurance model may be detriment for the policyholders of company. Also in this portfolio, with computing the conditional expectation of claims measure show that using the claims with Pareto distribution is not suitable in the estimation of claims. The estimation of conditional expectation of random variable of claims is computed by simulation method for some of the statistical distributions. The results are investigated with real examples.
Abouzar Bazyari, Morad Alizadeh,
Volume 16, Issue 1 (9-2022)
Abstract
In this paper, the collective risk model of an insurance company with constant surplus initial and premium when the claims are distributed as Exponential distribution and process number of claims distributed as Poisson distribution is considered. It is supposed that the reinsurance is done based on excess loss, which in that insurance portfolio, the part of total premium is the share of the reinsurer. A general formula for computing the infinite time ruin probability in the excess loss reinsurance risk model is presented based on the classical ruin probability. The random variable of the total amount of reinsurer's insurer payment in the risk model of excess loss reinsurance is investigated and proposed explicit formulas for calculating the infinite time ruin probability in the risk model of excess loss reinsurance. Finally, the results are examined for Lindley and Exponential distributions with numerical data.
Dr. Abouzar Bazyari,
Volume 16, Issue 2 (3-2023)
Abstract
In this paper, the individual risk model of the insurance company with dependent claims is considered and assumes that the binary vector of random variables of claim sizes is independent. Also, they have a common joint distribution function. A recursive formula for infinite time ruin probability is obtained according to the initial reserve and joint probability density function of random variables of claim sizes using probability inequalities and the induction method. Some numerical examples and simulation studies are presented for checking the results related to the light-tailed bivariate Poisson, heavy-tailed Log-Normal and Pareto distributions. The results are compared for Farlie–Gambel–Morgenstern and bivariate Frank copula functions. The effect of claims with heavy-tailed distributions on the ruin probability is also investigated.
Dr. Abouzar Bazyari,
Volume 17, Issue 1 (9-2023)
Abstract
In the excess loss reinsurance risk model, the amount of insurance premium paid by the company is influential in the ruin of that company. In this paper, the premium function is presented based on the expected amount of total payments of the reinsurer to the assigning insurer, the constraint on this function is investigated, and for the claims with any arbitrary distribution, the contour plots are drawn and with presenting optimization algorithm, infinite time ruin probability function will be minimum for different values of initial capital and threshold value. Finally, the excess loss reinsurance risk model with non-exponential claims is considered, and the infinite time ruin probability is calculated with numerical examples.
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