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

For a bivariate \Levy process $(\xi_t,\eta_t)_{t\geq 0}$ the generalised Ornstein-Uhlenbeck (GOU) process is defined as $$V_t:=e^{\xi_t}(z+\int_0^t e^{-\xi_{s-}} \eta_s), t\ge0,$$where $z\in\mathbb{R}.$ 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 \cite{BankovskySly08}, which stated conditions for zero probability of ruin, and completes a significant aspect of the study of the GOU

Where the right gets in: on Rawls’s criticism of Habermas's conception of legitimacy

Many commentators have failed to identify the important issues at the heart of the debate between Habermas and Rawls. This is partly because they give undue attention to differences between their respective devices of representation, the original position and principle (U), neither of which are germane to the actual dispute. The dispute is at bottom about how best to conceive of democratic legitimacy. Rawls indicates where the dividing issues lie when he objects that Habermas’s account of democratic legitimacy is comprehensive and his is confined to the political. But his argument is vitiated by a threefold ambiguity in what he means by “comprehensive doctrine.” Tidying up this ambiguity helps reveal that the dispute turns on the way in which morality relates to political legitimacy. Although Habermas calls his conception of legitimate law “morally freestanding”, and as such distinguishes it from Kantian and Natural Law accounts of legitimacy, it is not as freestanding from morality as he likes to present it. Habermas’s mature theory contains conflicting claims about relation between morality and democratic legitimacy. So there is at least one important sense in which Rawls's charge of comprehensiveness is made to stick againstHabermas’s conception of democratic legitimacy, and remains unanswered

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

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) whi

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

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 define necessary and sufficient conditions under which the infin

Exact conditions for no ruin for the generalised OrnsteinUhlenbeck process

For a bivariate Lévy process (ξt,ηt)t≥0 the generalised Ornstein-Uhlenbeck (GOU) process is defined as Vt: = e ξt z + ∫ t 0 e −ξs− dηs, 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

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

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.Lévy processes Generalised Ornstein-Uhlenbeck process Exponential functionals of Lévy processes Ruin probability