New Representation for Non Ruin Probability of Insurance Model with Rent Contracts and Its Application for Assessment of Critical Risks

Authors

  • Artak R. Martirosyan Institute for Informatics and Automation Problems of NAS RA

Keywords:

Insurance, rent, regular variation, heavy traffic, critical risks, integrodifferential equation

Abstract

The paper considers the particular solution of one integro-differential equation of insurance risk theory. New representation for that solution is found, which is used for assessment of critical risks of the insurance companies that conduct purely rent operations. The critical risks are found in the case of a heavy traffic and regular tail variation of the insurance premiums distribution function.

References

L. Takach, Combinatorial methods in the random process theory (Mir, Moscow, 1971).

T. Saxen, On the probability of ruin in the collective risk theory for insurance enterprises with only negative risk sums, (Skand. Akt., 31, pp. 199-228, 1948).

T. Saxen, Sur les mouvements aleatoires et le problem de ruine de la theorie du risque collective, (Soc. Sci. Fenn. Comm. Phys. Math., 16, pp. 1-55, 1951).

A.R. Martirosyan, "Critical risks in models of collective insurance", Actuary, N3, 2009 (in Russian, see www:actuaries:ru=magazine=?SECTIONID=411).

A.G. Sholomickiy, "Risk theory: choice at the uncertainty and risk modeling", M.:, 2005.

E. Seneta, Regularly varying functions (Nauka, Moscow, 1985).

A.M. Sedletskii, Analytic fourier transforms and exponential approximations, Series: Contemporary Mathematics, Fundamental Directions 5 (Moscow, 2003).

V. Feller, Introduction to probability theory and its applications 2 (Mir, Moscow, 1984).

A.R. Martirosyan, ”The asymptotic analysis of the characteristics of the insurance models in critical situations", Dissertation of candidate of physical and mathematical sciences, Yerevan, 2008 (see Electronic journal differential equations and control processes, http://www.math.spbu.ru/diffjournal/RU/numbers/2008.3/issue.html,orhttp://www.prorector.org/avtors/martirosyan/diss.pdf).

E.A. Danielian, "Limit theorems for waiting time in single-channel systems", Reports of Academy of Sciences of Armenia, vol. LXXI, N3, pp. 129-135, 1980.

V.G. Saakyan, "Random choice discipline in models ¡!Mrj¡!Grj1j1", M.: Dissertation for physical and mathematical sciences, 1985.

E.A. Danielian, R.N. Chitchyan, "Multidimensional limit theorems for the waiting time in priority queues of ¡!Mrj¡!Grj1j1 type", Acta Cybernetica, vol. 5, Fasc 3, pp. 325-343, Szeged, 1981.

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Published

2021-12-10

How to Cite

Martirosyan, A. R. . (2021). New Representation for Non Ruin Probability of Insurance Model with Rent Contracts and Its Application for Assessment of Critical Risks. Mathematical Problems of Computer Science, 36, 70–78. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/268