On The Ruin Problem With Investment When The Risky Asset Is A Semimartingale

Lioudmila Vostrikova and J\'er\^ome Spielmann
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Lioudmila Vostrikova: LAREMA
J\'er\^ome Spielmann: LAREMA

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Abstract: In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{\'e}vy 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 L{\'e}vy 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.

Date: 2018-06
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1806.11290

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