2009/04/24 by Erik J. Baurdoux, E. J. Baurdoux, A. E. Kyprianou +6
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G40 #60J99 #91B70 #Applied mathematics #Brownian motion #Exponential function #FOS: Mathematics #Mathematical analysis #Mathematical economics #Mathematical optimization #Mathematics #Optimal stopping #Optimization and Control (math.OC) #Physics #Probability (math.PR) #Probability and Risk Models #Statistical physics #Statistics #Stochastic process #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Wiener process #math.OC #math.PR #msc:60G40 #msc:60J99 #msc:91B70
paper · pdf · doi:10.48550/arxiv.0904.3871
arxiv created 2009/04/24 · openalex publication_date 2009/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In Gapeev and Kühn (2005), the stochastic 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 occurence of continuous and smooth fit. In Gapeev and Kühn (2005), 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.