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

Author

Listed:
  • Jérôme Spielmann

    (LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique)

  • Lioudmila Vostrikova

    (LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Jérôme Spielmann & Lioudmila Vostrikova, 2019. "On The Ruin Problem With Investment When The Risky Asset Is A Semimartingale," Working Papers hal-01825317, HAL.
    • Handle: RePEc:hal:wpaper:hal-01825317
    Note: View the original document on HAL open archive server: https://hal.science/hal-01825317v2
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