Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155975 | Stochastic Processes and their Applications | 2011 | 24 Pages |
Abstract
In Gapeev and Kühn (2005) [8], the Dynkin game corresponding to perpetual convertible bonds was considered, when driven by a Brownian motion and a compound Poisson process with exponential jumps. We consider the same stochastic game but driven by a spectrally positive Lévy process. We establish a complete solution to the game indicating four principle parameter regimes as well as characterizing the occurrence of continuous and smooth fit. In Gapeev and Kühn (2005) [8], the method of proof was mainly based on solving a free boundary value problem. In this paper, we instead use fluctuation theory and an auxiliary optimal stopping problem to find a solution to the game.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
E.J. Baurdoux, A.E. Kyprianou, J.C. Pardo,