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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, semimartingale, upper and lower estimates, logarithmic asymptotic, ruin with probability 1.
Mots-clés : Lévy process 
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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/

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