Another approach to the problem of
Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 1-18.

Voir la notice de l'article provenant de la source Math-Net.Ru

An exponential estimate of ruin probability for an insurance company which invests all its capital in risk assets is found. The process which describes the risky assets is assumed to follow a geometrical Brownian motion. Insurance premium flow depends on the value of reserves of the insurance company. The problem is solved by reduction of the generalized risk process to the classical risk process without investments.
Keywords: Ruin process, ruin probability, geometrical Brownian motion, supermartingale approach.
@article{THSP_2007_13_4_a0,
     author = {Maryna Androshchuk and Yuliya Mishura},
     title = {Another approach to the problem of},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {1--18},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a0/}
}
TY  - JOUR
AU  - Maryna Androshchuk
AU  - Yuliya Mishura
TI  - Another approach to the problem of
JO  - Teoriâ slučajnyh processov
PY  - 2007
SP  - 1
EP  - 18
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a0/
LA  - en
ID  - THSP_2007_13_4_a0
ER  - 
%0 Journal Article
%A Maryna Androshchuk
%A Yuliya Mishura
%T Another approach to the problem of
%J Teoriâ slučajnyh processov
%D 2007
%P 1-18
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a0/
%G en
%F THSP_2007_13_4_a0
Maryna Androshchuk; Yuliya Mishura. Another approach to the problem of. Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 1-18. http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a0/

[1] A. G. Frolova, Yu.Ṁ. Kabanov, S. M. Pergamenshchikov, “In the Insurance Business Risky Investments are Dangerous”, Finance and Stochastics, 6:2 (2002), 227–235

[2] J. Grandell, Aspects of Risk Theory, Springer-Verlag, New York, 1991

[3] R. J. Elliott, Stochastic Calculus and Applications, Springer, New York, 1982

[4] I. I. Gikhman, A. V. Skorokhod, Stochastic Differential Equations, Naukova Dumka, Kiev, 1968 (Rus.)

[5] P. E. Protter, Stochastic Integration and Differential Equations, Springer, Berlin, 2004

[6] A. V. Skorokhod, Random Processes with Independent Increments, Nauka, Moscow, 1986 (Rus.)

[7] J. Gaier, P. Grandits, W. Schachermayer, “Asymptotic Ruin Probabilities and Optimal Investment”, The Annals of Applied Probability, 13 (2003), 1054–1076

[8] M. O. Androshchuk, Yu. S. Mishura, “An Estimate of Ruin Probability for an Insurance Company which is Functioning on $BS$-market”, Ukrainian Mathematical Journal, 11 (2007) (Ukr)