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Ruin probability for an insurer investing in several risky assets
Author(s):
M.
V.
Bratyk
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 77
(2007).
Journal:
Theor. Probability and Math. Statist.
No. 77
(2008),
1-13.
MSC (2000):
Primary 60G44, 60H30;
Secondary 62P05, 60K10
Posted:
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.
References:
-
- 1.
- J. Gaier, P. Grandits, and W. Schachermayer, Asymptotic ruin probabilities and optimal investment, Ann. Appl. Probab. 13 (2003), no. 3, 1054-1076. MR 1994044 (2004k:91124)
- 2.
- Yu. S. Mishura, An estimate for the ruin probability for models with long-term dependence, Teor. Imovir. Mat. Stat. 72 (2005), 93-100; English transl. in Theory Probab. Math. Statist. 72 (2006), 103-111. MR 2168140 (2007b:60164)
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- A. V. Mel'nikov, Risk Analysis in Finance and Insurance, Chapman and Hall/CRC, 2004. MR 2013235 (2004i:91004)
- 4.
- A. V. Mel'nikov, Risk Management. Stochastic Analysis of Risks in Finance and Insurance, ``Ankil'', Moscow, 2001. (Russian)
- 5.
- A. V. Boikov, The Cramér-Lundberg model with stochastic premiums, Teor. Veroyatnost. i Primenen. 47 (2002), no. 3, 549-553; English transl. in Theory Probab. Appl. 47 (2003), no. 3, 489-493. MR 1975908 (2004d:60228)
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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:
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):
17/JUL/2006
Posted:
January 14, 2009
Copyright of article:
Copyright
2008,
American Mathematical Society
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