A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically from finance, especially for path-dependent option...

Applying excursion theory, we re-express several well studied fluctuation quantities associated to Parisian ruin problem for L´evy risk processes in terms of integrals with respect to excursion measure for spectrally negative L´evy process. We show that these new expressions reconcile with the...

Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and...

This paper considers magnitude, asymptotics and duration of drawdowns for some Levy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Levy processes using an approximation approach. For any spectrally negative Levy process whose scale...

Drawdowns measuring the decline in value from the historical running maxima over a given period of time, are considered as extremal events from the standpoint of risk management. To date, research on the topic has mainly focus on the side of severity by studying the first drawdown over certain...

In ruin theory, an insurer’s income process is usually assumed to grow at a deterministic rate of c 0 over time. For instance, both the well-known Cramér-Lundberg risk process and the Sparre Andersen risk model have this assumption built in the construction of their respective surplus...

Drawdowns measuring the decline in value from the historical running maxima over a given period of time, are considered as extremal events from the standpoint of risk management. To date, research on the topic has mainly focus on the side of severity by studying the first drawdown over certain...