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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Ruin probability for an insurer investing in several risky assets


Author: M. V. Bratyk
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
Journal: Theor. Probability and Math. Statist. 77 (2008), 1-13
MSC (2000): Primary 60G44, 60H30; Secondary 62P05, 60K10
Published electronically: January 14, 2009
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Abstract: The ruin probability of an insurer is studied for the classical Cramér-Lundberg model with finite exponential moments. The nonclassical property of the model considered in the paper is the possibility to invest in two different risky assets (which may be dependent) whose price processes are either described by geometric Brownian motions or are semimartingales with absolutely continuous characteristics with respect to Lebesgue measure. We study the ruin probability for the case where a free credit is not available in the money market and where the insurer can invest in a finite number of risky assets whose price processes are described by jointly independent Brownian motions.


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Additional Information

M. V. Bratyk
Affiliation: Department of Mathematics, Faculty for Informatics, National Kyiv Mohyla University, Skovoroda Street, 2, Kyiv, 04070, Ukraine
Email: mbratyk@ukr.net

DOI: http://dx.doi.org/10.1090/S0094-9000-08-00743-6
PII: S 0094-9000(08)00743-6
Keywords: Cram\'er--Lundberg model, ruin probability, investment strategy, geometric Brownian motion
Received by editor(s): July 17, 2006
Published electronically: January 14, 2009
Article copyright: © Copyright 2008 American Mathematical Society