scholarly journals General drawdown of general tax model in a time-homogeneous Markov framework

2021 ◽  
Vol 58 (4) ◽  
pp. 1131-1151
Author(s):  
Florin Avram ◽  
Bin Li ◽  
Shu Li
Keyword(s):  
Markov Process ◽  
Optimal Stopping ◽  
Mathematical Finance ◽  
Levy Processes ◽  
Free Time ◽  
First Passage ◽  
Homogeneous Markov Process ◽  
Cusum Procedure ◽  
Optimal Stopping Problems ◽  
Spectrally Negative Lévy Processes

AbstractDrawdown/regret times feature prominently in optimal stopping problems, in statistics (CUSUM procedure), and in mathematical finance (Russian options). Recently it was discovered that a first passage theory with more general drawdown times, which generalize classic ruin times, may be explicitly developed for spectrally negative Lévy processes [9, 20]. In this paper we further examine the general drawdown-related quantities in the (upward skip-free) time-homogeneous Markov process, and then in its (general) tax process by noticing the pathwise connection between general drawdown and the tax process.

From Disorder Detection to Optimal Stopping and Mathematical Finance

2010 ◽  
Vol 29 (2) ◽  
pp. 112-124
Author(s):  
Robert Liptser ◽  
Alexander G. Tartakovsky
Keyword(s):  
Optimal Stopping ◽  
Mathematical Finance

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Adjoint Operator ◽  
Integral Kernel ◽  
Mathematical Finance ◽  
Elliptic Operators ◽  
Complete Analysis ◽  
Time Behavior ◽  
Degenerate Elliptic Operators ◽  
Regularity Properties ◽  
Degenerate Elliptic ◽  
Mathematical Foundations

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

Paris-Princeton Lectures on Mathematical Finance 2010

2011 ◽  
Author(s):  
Areski Cousin ◽  
Stéphane Crépey ◽  
Olivier Guéant ◽  
David Hobson ◽  
Monique Jeanblanc ◽  
...  
Keyword(s):  
Mathematical Finance
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