On One-Sided Stochastic Games and Their Applications to Finance

Abstract

The present article continues the work initiated in Dshalalow and Huang^{[ 5 ]} about an antagonistic stochastic game. The main phase of that game was preceded by “unprovoked” hostile actions by one of the players. We assert that the result in Dshalalow and Huang provide a closed form solution by working on a particular case and by arriving at fully explicit formulas for associated distributions. A new density function for the related processes has been obtained: a product of a negative exponential and modified Bessel functions. Other investigation is rendered for pre-exit functionals. The analyticity of the formulas are illustrated by numerical examples.

Keywords:

• Compound Poisson process
• Exit time
• First passage time
• Fluctuation theory
• Marked point process
• Random walk analysis
• Ruin time
• Stochastic games
• Stochastic finance
• Stock market

AMS Subject Classification:

• 82B41
• 60G51
• 60G55
• 60G57
• 91A10
• 91A05
• 91A60
• 60K05

Acknowledgments

This article is part of the Special Issue in honor of Marcel F. Neuts, published in volume 27(4) of Stochastic Models.

This article is dedicated to Marcel Neuts, whom I am honored to know for many years and whose exceptional contributions to science are revered worldwide.

This research is supported by the US Army Grant No. W911NF-07-1-0121.