Diploma Thesis from the year 2011 in the subject Mathematics - Stochastics, grade: 1,0, Humboldt-University of Berlin (Mathematik), language: English, abstract: This diploma thesis is concerned with backward stochastic differential equations (BSDEs) with jumps which are driven by a Brownian Motion and a random measure. We derive existence and uniqueness results for bounded solutions to such BSDEs when the generator posses a certain monotonicity property instead of the usual global Lipschitz condition. Starting with results in the case of finite activity, considering generators of difference type and showing a comparison theorem, allows us to advance to the case of infinite activity.
On Backward Stochastic Differential Equations (BSDEs) with jumps of infinite activity
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Diploma Thesis from the year 2011 in the subject Mathematics - Stochastics, grade: 1,0, Humboldt-University of Berlin (Mathematik), language: English, abstract: This diploma thesis is concerned with backward stochastic differential equations (BSDEs) with jumps which are driven by a Brownian Motion and a random measure. We derive existence and uniqueness results for bounded solutions to such BSDEs when the generator posses a certain monotonicity property instead of the usual global Lipschitz condition. Starting with results in the case of finite activity, considering generators of difference type and showing a comparison theorem, allows us to advance to the case of infinite activity.
This book consists of four chapters. In first chapter there is a short review of theory of Backward Stochastic Differential Equations (BSDEs) and Bounded Mean Oscillation (BMO) martingales. In...
Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of...
In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical...
This book provides a compact exposition of the results explaining interrelations between diffusion stochastic processes, SDEs and the fractional infinitesimal operators. The draft of this book has...
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