Tempered stable processes have emerged as a crucial class of stochastic models, blending the heavy‐tail characteristics of stable laws with an exponential dampening mechanism that ensures finite ...

For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process.

Abstract. This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward equation ...