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

2008/04/10 by Damien Bankovsky, Bankovsky, Damien, Allan Sly +1
Decision Sciences · Economics, Econometrics and Finance · #60H30 #60J25 #91B30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0804.1634

openalex publication_date 2008/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a bivariate Lévy process (ξ_t,η_t)_{t≥ 0} the generalised Ornstein-Uhlenbeck (GOU) process is defined as V_t:=e^ξ_t(z+∫₀^t e^-ξ_s-dη_s), t≥0, where z∈ℝ. 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 ξ and η. We also present technical results which explain the structure of the lower bound of the GOU.

Citations

• A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour

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