TY - JOUR
T1 - Conditions for certain ruin for the generalised Ornstein-Uhlenbeck process and the structure of the upper and lower bounds
AU - Bankovsky, Damien
PY - 2010/2
Y1 - 2010/2
N2 - For a bivariate Lévy process (ξt, ηt)t ≥ 0 the generalised Ornstein-Uhlenbeck (GOU) process is defined as Vt {colon equals} eξt (z + ∫0t e- ξs - d ηs), t ≥ 0, where z ∈ R. We present conditions on the characteristic triplet of (ξ, η) 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.
AB - For a bivariate Lévy process (ξt, ηt)t ≥ 0 the generalised Ornstein-Uhlenbeck (GOU) process is defined as Vt {colon equals} eξt (z + ∫0t e- ξs - d ηs), t ≥ 0, where z ∈ R. We present conditions on the characteristic triplet of (ξ, η) 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.
KW - Exponential functionals of Lévy processes
KW - Generalised Ornstein-Uhlenbeck process
KW - Lévy processes
KW - Ruin probability
UR - http://www.scopus.com/inward/record.url?scp=72549115612&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2009.11.003
DO - 10.1016/j.spa.2009.11.003
M3 - Article
SN - 0304-4149
VL - 120
SP - 255
EP - 280
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -