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This article is cited in 1 scientific paper (total in 1 paper)
On the ruin problem with investment when the risky asset is a semimartingale
J. Spielmann, L. Vostrikova LAREMA, Département de Mathématiques, Université d'Angers, France
Abstract:
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.
Received: 07.10.2018
Citation:
J. Spielmann, L. Vostrikova, “On the ruin problem with investment when the risky asset is a semimartingale”, Teor. Veroyatnost. i Primenen., 65:2 (2020), 312–337; Theory Probab. Appl., 65:2 (2020), 249–269
Linking options:
https://www.mathnet.ru/eng/tvp5355https://doi.org/10.4213/tvp5355 https://www.mathnet.ru/eng/tvp/v65/i2/p312
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Abstract page: | 241 | Full-text PDF : | 34 | References: | 24 | First page: | 2 |
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