Dual Laplace - Stieltjes Transformations of Critical Risks in Case of Negative Insurance Payments
Abstract
The present paper is devoted to critical risks of collective insurance models with negative insurance payments (connected with contracts with usual life rent). Limit theorems arisen in critical situations are represented and the dual Laplass-Stiltjes transformations are found for critical risks arisen in collective insurance risks models with negative insurance payments. The specifications of the considered collective risk model and the adaptive control strategy for multiperiodic insurance risk model introduced by Malinovskii is illustrated.
References
L. Takach,Combinatorial methods in the random processes theory, (in Russian), Mir, Moscow, 1971.
T. Saxen, “On the probability of ruin the collective risk theory for insurance enterprises with only negative risk sums", Skand. Akt., vol. 31, pp. 199-228, 1948.
T. Saxen, “Sur les mouvements aleatoires et le problem de ruine de la theorie du risqué collective", Soc sci fenn comm. Phys math, num. 16, pp. 1-55, 1951.
G. Arfwedson, “A semi-convergent series with application to the collective theory of risk", Skand. Akt., vol. 35, pp. 16-35, 1952.
V.K. Malinovskii, “On a non-linear dynamic solvency control model", In: Contribution to: XXXIV ASTIN Colloquium, Berlin, pp. 24-27, 2003.
V.K. Malinovskii, “Adaptive control strategies and dependence of finite time ruin on the premium loading", Insurance: Mathematics and Economics, vol. 42, pp. 81-94, 2008.
A.R. Martirosyan, The asymptotic analysis of the characteristics of the insurance models in critical situations, www.neva.ru/journal/j/EN/numbers/2008.3/article.80.html or www.prorector.org/avtors/martirosyan/diss.pdf, (in Russian), Yerevan, Dissertation, 2008.
N.U. Prabghu, The methods of theory of queue and reserves control, (in Russian), M., Mashinostroenie, 1969.
N.U. Prabghu, Stochastic processes of theory of reserves, (in Russian), M., Mir, 1984.
A.R. Martirosyan, “Critical risks in insurance portfolios", (in Russian), Yerevan: Mathematics in Higher School, vol. 3, no. 4, pp. 10-17, 2007.
W. Feller, Introduction to probability theory and its application, (in Russian), M., Mir, vol. 2, 1984.
A.G. Sholomickiy, Risk theory: choice at the ancertainty and risk modeling, (in Russian), M., 2005.
A.R. Martirosyan, “Critical risks in models of collective insurance", Actuary: Informational-analitical bulletin, no. 3, www:actuaries:ru=magazine=?SECTIONID=411, (in Russian), 2009.
V. Corolev, I. Sokolov, A. Gordeev, M. Grigoreva, S. Popov, N. Chebonenko, “Some forecasting methods of interim characteristic of risks connected with catastrophic events", (in Russian), Actuary: Informational-analytical bulletin, no. 1, pp. 34-40, 2007.
A.N. Shiryaev, Foundations of stochastic financial mathematics, (in Russian), M., FAZIS, vol. 1, 1998.
A.A. Borovkov, Theory of probabilities, (in Russian), M., Nauka, 1986.
E.A. Danielian, “Limit theorems for waiting time in single-channel systems", (in Russian), Reports of Academy of Sciences of Armenia, vol. LXXI, no. 3, pp. 129-135, 1980.
V.G. Saakyan, “Random choice discipline in models ¡!Mrj¡!Grj1j1", (in Russian), M., Dissertation, 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.
V.M. Zolotarev, One-dimensional stable distributions, (in Russian), M., Nauka, 1980.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
