ON THE RUIN PROBLEM WITH INVESTMENT WHEN THE RISKY ASSET IS A SEMIMARTINGALE

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. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases. When R is a Lévy process, we retrieve the well-known results. Then, we show that these bounds are asymptotically optimal in the finite time case, under some simple conditions on the characteristics of X. Finally, we obtain a condition for ruin with probability one when X is a Brownian motion with negative drift and express it explicitly using the characteristics of R.
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Submitted on : Friday, March 22, 2019 - 4:52:01 PM
Last modification on : Friday, May 10, 2019 - 12:14:02 PM
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  • HAL Id : hal-01825317, version 2
  • ARXIV : 1806.11290

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Jérôme Spielmann, Lioudmila Vostrikova. ON THE RUIN PROBLEM WITH INVESTMENT WHEN THE RISKY ASSET IS A SEMIMARTINGALE. 2019. ⟨hal-01825317v2⟩

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