An exact solution of the risk equation with a step current reserve function
Author:
D. P. Kerekesha
Translated by:
Oleg Klesov
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 Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We obtain explicitly the solution of the risk equation for a step current reserve function.
References
- Søren Asmussen, Ruin probabilities, Advanced Series on Statistical Science & Applied Probability, vol. 2, World Scientific Publishing Co., Inc., River Edge, NJ, 2000. MR 1794582
- D. Kerekesha, Some generalization of the ruin probability problem in the classical risk theory, Theory Stoch. Process. 7 (23) (2001), no. 2, 189–195.
- 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
- N. I. Akhiezer, Lektsii ob integral′nykh preobrazovaniyakh, “Vishcha Shkola”, Khar′kov, 1984 (Russian). MR 805538
- Lajos Takács, Combinatorial methods in the theory of stochastic processes, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0217858
- V. A. Trenogin, Funktsional′nyĭ analiz, “Nauka”, Moscow, 1980 (Russian). MR 598629
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959
References
- S. Asmussen, Ruin Probabilities, Advanced Series on Statistical and Applied Probability, World Scientific, Singapore, 2000. MR 1794582 (2001m:62119)
- D. Kerekesha, Some generalization of the ruin probability problem in the classical risk theory, Theory Stoch. Process. 7 (23) (2001), no. 2, 189–195.
- P. Koosis, Introduction to $H^p$ Spaces, 2nd ed., Cambridge University Press, Cambridge, 1998. MR 1669574 (2000b:30052)
- N. I. Akhiezer, Lectures on Integral Transforms, “Vyshcha Shkola”, Kharkiv, 1984; English transl., Amer. Math. Soc., Providence, RI, 1988. MR 0805538 (87c:44001)
- L. Takács, Combinatorial Methods in the Theory of Stochastic Processes, Wiley, New York–London–Sydney, 1967. MR 0217858 (36:947)
- V. A. Trenogin, Functional Analysis, “Nauka”, Moscow, 1980. (Russian) MR 0598629 (82k:46001)
- M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. 1, 2nd ed. Academic Press, New York, 1980. MR 0751959 (85e:46002)
Similar Articles
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
Received by editor(s):
October 14, 2002
Published electronically:
February 7, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
