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  5. The parametric type decision of the direct and inverse problems of bankruptcy of the insurance company for the individual risk model

The parametric type decision of the direct and inverse problems of bankruptcy of the insurance company for the individual risk model

V. Dubnytskyi, I. Skorikova, H. Fesenko, I. Cherepnov
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Description: The relevance of the task for insurance of risks associated with agricultural activities is shown. The main assumptions when solving the problem are as follows: the analyzed situation is related only to annual insurance payments. The number of participants in the insurance process is not accidental and is not changed during the period under review. Insurance premium is paid in full at the beginning of the analyzed period. For each insurance contract, the statistical properties of the individual losses of the insurance company as a result of payments under this insurance event are known. Disasters, that are similar to simultaneous occurrence of insurance cases under several contracts, are excluded from consideration. The condition for the successful operation of the insurance company is that the amount of the company's assets is equal to the amount of insurance premiums and equity should exceed the amount of insurance payments at a given time interval. The probability of non-bankruptcy of the insurance company is equal to the probability of the event that the amount of insurance payments don not exceed the sum of the assets of the insurance company. The probability of bankruptcy of the insurance company is equal to the probability of the opposite event - the probability of non-bankruptcy of the insurance company. Evaluating the risk of bankruptcy of an insurance company is called a direct problem, evaluating the risk of non-bankruptcy of an insurance company is called the direct problem for insurance of risks. The decision for both a principle of expected value and a principle of standard deviation are chosen as methods for solving the formulated problems. The principle of the expected value is the amount of assets of the insurance company necessary for its successful operation and equal to a multiple of the average value of insurance payments. The standard deviation principle is the value of the assets of the insurance company necessary for its successful operation and equal to the sum of the average value and a multiple of the standard deviation of insurance payments. The direct problem of bankruptcy of an insurance company is a problem whose solution determines the probability of successful activity of an insurance company under certain laws of distribution for the amount of insurance payments. The reverse problem of bankruptcy of an insurance company is the problem whose solution determines the amount of assets that provide the given probability of non-bankruptcy (bankruptcy) of the insurance company. The solution of this problem is considered for the following types of distribution laws: normal distribution, log-normal distribution, gamma distribution, Weibull distribution, inverse Gaussian distribution, Pareto distribution.


Keywords: the problem of bankruptcy of an insurance company, the principle of mathematical expectation, the standard deviation, normal distribution, log-normal distribution, gamma distribution, Weibull distribution, inverse Gaussian distribution, Pareto distribution

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Reference:
 Dubnytskyi, V.Yu., Skorykova, Y.H., Fesenko, H.V. and Cherepnev, Y.A. (2019), “Reshenye v parametrycheskom vyde priamoi y obratnoi zadachy o razorenyy strakhovoi kompanyy dlia modely yndyvydualnoho ryska” [The parametric type decision of the direct and inverse problems of bankruptcy of the insurance company for the individual risk model], Information Processing Systems, Vol. 1(156), pp. 50-57. https://doi.org/10.30748/soi.2019.156.07.