Abstract
The authors, using the simulation procedure based on Cramer-Lundberg model, have conducted study of dependence of the initial insurance reserve on the intensity of insurance premiums for different types of distribution of periods and amounts of insurance payments while ensuring high probability of non-bankruptcy of an insurance company.
Taking into account that the probability of the company bankruptcy has a quantitative assessment of the possible occurrence of the event, one should consider a number of factors, i.e. the insurance premium amount, and the amount of the insurance reserve. Making up the projection probability of ruin under different scenarios of loss occurrence eventually allows to develop optimal management policy of the insurance company. The procedure of simulation modeling based on the model of Cramer-Lundberg for describing distributions of periods between the losses, and size of insurance benefits is based on the following types of distributions of random variables: exponential, truncated exponential, Erlang distribution and the Pareto distribution.
Analysis allows to the following conclusion:
- To describe the time intervals between successive losses which occur infrequently at a predetermined average intensity exponential distribution is most applicable.
- For more frequent loss occurrences the truncated exponential distribution should be used.
- Erlang model proposes that the intensity of the events can be either increasing or decreasing.
- Pareto distribution is used for describing insurance of catastrophic risks.
The conducted research proves that the chosen theoretical law of distribution of periods and amounts of insurance benefits can significantly affect the final forecast of financial stability of an insurance company and the choice of the initial insurance reserve.
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