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Conditions for certain ruin for the generalised Ornstein-Uhlenbeck process and the structure of the upper and lower bounds

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  • Bankovsky, Damien

Abstract

For a bivariate Lévy process ([xi]t,[eta]t)t>=0 the generalised Ornstein-Uhlenbeck (GOU) process is defined as where . We present conditions on the characteristic triplet of ([xi],[eta]) which ensure certain ruin for the GOU. We present a detailed analysis on the structure of the upper and lower bounds and the sets of values on which the GOU is almost surely increasing, or decreasing. This paper is the sequel to Bankovsky and Sly (2008) [2], which stated conditions for zero probability of ruin, and completes a significant aspect of the study of the GOU.

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  • 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.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:2:p:255-280
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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.
    2. 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.
    3. 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.
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