Geodesic
On the ruin problem with investment when the risky asset is a~semimartingale
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 312-337

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In this paper, we study the ruin problem with investment in a general framework where the business part $X$ is a Lévy process and the return on investment $R$ is a semimartingale. Under some conditions, we obtain upper and lower bounds on the finite and infinite time ruin probabilities as well as the logarithmic asymptotic for them. When $R$ is a Lévy process, we retrieve some well-known results. Finally, we obtain conditions on the exponential functionals of $R$ for ruin with probability $1$, and we express these conditions using the semimartingale characteristics of $R$ in the case of Lévy processes.
Keywords: ruin probability, investment, Lévy process, semimartingale, upper and lower estimates, logarithmic asymptotic, ruin with probability 1. 
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     author = {J. Spielmann and L. Vostrikova},
     title = {On the ruin problem with investment when the risky asset is a~semimartingale},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {312--337},
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a3/}
}
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J. Spielmann; L. Vostrikova. On the ruin problem with investment when the risky asset is a~semimartingale. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 312-337. http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a3/