A note on \(r\)-balayages of matrix-exponential Lévy processes. (English) Zbl 1189.60153

Sheu, Yuan-Chung; Chen, Yu-Ting

Electron. Commun. Probab. 14, 165-175 (2009).

Summary: We give semi-explicit solutions for \(r\)-balayages of matrix-exponential-Lévy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the undershoot and a semi-explicit solution of the negative Wiener-Hopf factor. Our result is closely related to the works by E. Mordecki [Finance Stoch. 6, No. 4, 473–493 (2002; Zbl 1035.60038)], S. Asmussen, F. Avram and M. R. Pistorius [Stochastic Processes Appl. 109, No. 1, 79–111 (2004; Zbl 1075.60037)], Y. T. Chen, C. F. Lee and Y. C. Sheu [Finance Stoch. 11, No. 3, 323–355 (2007; Zbl 1164.60034)], and many others.

MSC:

60J75	Jump processes (MSC2010)
91B30	Risk theory, insurance (MSC2010)
91B70	Stochastic models in economics
91G20	Derivative securities (option pricing, hedging, etc.)

Keywords:

Lévy process; matrix-exponential distribution; first exit; balayage; ruin theory