ON THE RUIN PROBLEM WITH INVESTMENT WHEN THE RISKY ASSET IS A SEMIMARTINGALE - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2019

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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Dates and versions

hal-01825317 , version 1 (28-06-2018)
hal-01825317 , version 2 (22-03-2019)

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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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