Risk modelling on liquidations with Lévy processes

Highlights：

• Our paper represents the first attempt in studying the Liquidations under the Lévy setup.

• We compactly express the joint distribution of the time of liquidation, the surplus at liquidation and the historical high of the surplus until liquidation by the scale functions and Lévy triplets associated with two underlying Lévy processes. When the two Lévy processes are different from each other by a deterministic drift or coincide with each other, even more compact results expressed only by the scale functions are presented.

• Our results are very general and are consistent with the existing literatures on Parisian ruin with (or without) a lower barrier when our model and parameters degenerate.

• Numerical examples are provided to illustrate the underlying features of liquidation ruin.

摘要

•Our paper represents the first attempt in studying the Liquidations under the Lévy setup.•We compactly express the joint distribution of the time of liquidation, the surplus at liquidation and the historical high of the surplus until liquidation by the scale functions and Lévy triplets associated with two underlying Lévy processes. When the two Lévy processes are different from each other by a deterministic drift or coincide with each other, even more compact results expressed only by the scale functions are presented.•Our results are very general and are consistent with the existing literatures on Parisian ruin with (or without) a lower barrier when our model and parameters degenerate.•Numerical examples are provided to illustrate the underlying features of liquidation ruin.

论文关键词：Spectrally negative Lévy process,Liquidation time,Expected discounted penalty function,Discounted joint probability density,Liquidation probability