The McKean stochastic game driven by a spectrally negative Lévy process

The Shepp–Shiryaev stochastic game driven by a spectrally negative Lévy process

In [15], the stochastic-game-analogue of Shepp and Shiryaev’s optimal stopping problem (cf. [23] and [24]) was considered when driven by an exponential Brownian motion. We consider the same stochastic game, which we call the Shepp–Shiryaev stochastic game, but driven by a spectrally negative Lévy process and for a wider parameter range. Unlike [15], we do not appeal predominantly to stochastic ...

A Note on Scale Functions and the Time Value of Ruin for Lévy Insurance Risk Processes

We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important contributions of Zhou (2005) we provide an explicit characterization of a generalized version of the ...

The distribution of the supremum for spectrally asymmetric Lévy processes

In this article we derive formulas for the probability IP(supt≤T X(t) > u), T > 0 and IP(supt<∞X(t) > u) where X is a spectrally positive Lévy process with infinite variation. The formulas are generalizations of the well-known Takács formulas for stochastic processes with non-negative and interchangeable increments. Moreover, we find the joint distribution of inft≤T Y (t) and Y (T ) where Y is ...

Default Swap Games Driven by Spectrally Negative Lévy Processes∗

This paper studies game-type credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default termination. Under a structural credit risk model based on spectrally negative Lévy processes, we apply the principles of smooth and continuous fit to identif...

Fluctuation Theory and Stochastic Games for Spectrally Negative Lévy Processes