An exact solution of the risk equation with a step current reserve function

Author:
D. P. Kerekesha

Translated by:
Oleg Klesov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **69** (2003).

Journal:
Theor. Probability and Math. Statist. **69** (2004), 61-66

MSC (2000):
Primary 62P05; Secondary 42B30

DOI:
https://doi.org/10.1090/S0094-9000-05-00614-9

Published electronically:
February 7, 2005

MathSciNet review:
2110905

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We obtain explicitly the solution of the risk equation for a step current reserve function.

**1.**Søren Asmussen,*Ruin probabilities*, Advanced Series on Statistical Science & Applied Probability, vol. 2, World Scientific Publishing Co., Inc., River Edge, NJ, 2000. MR**1794582****2.**D. Kerekesha,*Some generalization of the ruin probability problem in the classical risk theory*, Theory Stoch. Process.**7**(**23**) (2001), no. 2, 189-195.**3.**Paul Koosis,*Introduction to 𝐻_{𝑝} spaces*, 2nd ed., Cambridge Tracts in Mathematics, vol. 115, Cambridge University Press, Cambridge, 1998. With two appendices by V. P. Havin [Viktor Petrovich Khavin]. MR**1669574****4.**N. I. Akhiezer,*Lectures on Integral Transforms*, ``Vyshcha Shkola'', Kharkiv, 1984; English transl., Amer. Math. Soc., Providence, RI, 1988. MR**0805538 (87c:44001)****5.**Lajos Takács,*Combinatorial methods in the theory of stochastic processes*, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR**0217858****6.**V. A. Trenogin,*Functional Analysis*, ``Nauka'', Moscow, 1980. (Russian) MR**0598629 (82k:46001)****7.**M. Reed and B. Simon,*Methods of Modern Mathematical Physics*, vol. 1, 2nd ed. Academic Press, New York, 1980. MR**0751959 (85e:46002)**

Retrieve articles in *Theory of Probability and Mathematical Statistics*
with MSC (2000):
62P05,
42B30

Retrieve articles in all journals with MSC (2000): 62P05, 42B30

Additional Information

**D. P. Kerekesha**

Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

DOI:
https://doi.org/10.1090/S0094-9000-05-00614-9

Received by editor(s):
October 14, 2002

Published electronically:
February 7, 2005

Article copyright:
© Copyright 2005
American Mathematical Society