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Exact conditions for no ruin for the generalised Ornstein-Uhlenbeck process

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  • Bankovsky, Damien
  • Sly, Allan

Abstract

For a bivariate Lévy process ([xi]t,[eta]t)t>=0 the generalised Ornstein-Uhlenbeck (GOU) process is defined as where . We define necessary and sufficient conditions under which the infinite horizon ruin probability for the process is zero. These conditions are stated in terms of the canonical characteristics of the Lévy process and reveal the effect of the dependence relationship between [xi] and [eta]. We also present technical results which explain the structure of the lower bound of the GOU.

Suggested Citation

  • Bankovsky, Damien & Sly, Allan, 2009. "Exact conditions for no ruin for the generalised Ornstein-Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2544-2562, August.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:8:p:2544-2562
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    References listed on IDEAS

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    1. Paulsen, Jostein, 1998. "Sharp conditions for certain ruin in a risk process with stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 135-148, June.
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    4. Nyrhinen, Harri, 2001. "Finite and infinite time ruin probabilities in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 265-285, April.
    5. Lindner, Alexander & Maller, Ross, 2005. "Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1701-1722, October.
    6. Patie, Pierre, 2005. "On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 593-607, April.
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    1. Bankovsky, Damien, 2010. "Conditions for certain ruin for the generalised Ornstein-Uhlenbeck process and the structure of the upper and lower bounds," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 255-280, February.

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