Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications PDF Download

Author: Łukasz Delong
Publisher: Springer Science & Business Media
ISBN: 1447153316
Category : Mathematics
Languages : en
Pages : 285

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Book Description
Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.

Author: Rong Situ
Publisher:
ISBN: 9787535925206
Category : Stochastic differential eqations
Languages : en
Pages : 333

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Book Description

Author: Rong SITU
Publisher: Springer Science & Business Media
ISBN: 0387251758
Category : Technology & Engineering
Languages : en
Pages : 444

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Book Description
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 SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

Author: Jin Ma
Publisher: Springer
ISBN: 3540488316
Category : Mathematics
Languages : en
Pages : 285

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Book Description
This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

Author: Rym Salhi
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
This thesis focuses on backward stochastic differential equation with jumps and their applications. In the first chapter, we study a backward stochastic differential equation (BSDE for short) driven jointly by a Brownian motion and an integer valued random measure that may have infinite activity with compensator being possibly time inhomogeneous. In particular, we are concerned with the case where the driver has quadratic growth and unbounded terminal condition. The existence and uniqueness of the solution are proven by combining a monotone approximation technics and a forward approach. Chapter 2 is devoted to the well-posedness of generalized doubly reflected BSDEs (GDRBSDE for short) with jumps under weaker assumptions on the data. In particular, we study the existence of a solution for a one-dimensional GDRBSDE with jumps when the terminal condition is only measurable with respect to the related filtration and when the coefficient has general stochastic quadratic growth. We also show, in a suitable framework, the connection between our class of backward stochastic differential equations and risk sensitive zero-sum game. In chapter 3, we investigate a general class of fully coupled mean field forward-backward under weak monotonicity conditions without assuming any non-degeneracy assumption on the forward equation. We derive existence and uniqueness results under two different sets of conditions based on proximation schema weither on the forward or the backward equation. Later, we give an application for storage in smart grids.

Author: N El Karoui
Publisher: CRC Press
ISBN: 9780582307339
Category : Mathematics
Languages : en
Pages : 236

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Book Description
This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Author: Stephane Crepey
Publisher: Springer Science & Business Media
ISBN: 3642371132
Category : Computers
Languages : en
Pages : 464

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Book Description
Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes. It also contains a review of quantitative finance tools, including Fourier techniques, Monte Carlo methods, finite differences and model calibration schemes. With a view to use in graduate courses in computational finance and financial modeling, corrected problem sets and Matlab sheets have been provided. Stéphane Crépey’s book starts with a few chapters on classical stochastic processes material, and then... fasten your seatbelt... the author starts traveling backwards in time through backward stochastic differential equations (BSDEs). This does not mean that one has to read the book backwards, like a manga! Rather, the possibility to move backwards in time, even if from a variety of final scenarios following a probability law, opens a multitude of possibilities for all those pricing problems whose solution is not a straightforward expectation. For example, this allows for framing problems like pricing with credit and funding costs in a rigorous mathematical setup. This is, as far as I know, the first book written for several levels of audiences, with applications to financial modeling and using BSDEs as one of the main tools, and as the song says: "it's never as good as the first time". Damiano Brigo, Chair of Mathematical Finance, Imperial College London While the classical theory of arbitrage free pricing has matured, and is now well understood and used by the finance industry, the theory of BSDEs continues to enjoy a rapid growth and remains a domain restricted to academic researchers and a handful of practitioners. Crépey’s book presents this novel approach to a wider community of researchers involved in mathematical modeling in finance. It is clearly an essential reference for anyone interested in the latest developments in financial mathematics. Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative Finance

Author: Situ Rong
Publisher: CRC Press
ISBN: 9781584881254
Category : Mathematics
Languages : en
Pages : 228

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Book Description
Many important physical variables satisfy certain dynamic evolution systems and can take only non-negative values. Therefore, one can study such variables by studying these dynamic systems. One can put some conditions on the coefficients to ensure non-negative values in deterministic cases. However, as a random process disturbs the system, the components of solutions to stochastic differential equations (SDE) can keep changing between arbitrary large positive and negative values-even in the simplest case. To overcome this difficulty, the author examines the reflecting stochastic differential equation (RSDE) with the coordinate planes as its boundary-or with a more general boundary. Reflecting Stochastic Differential Equations with Jumps and Applications systematically studies the general theory and applications of these equations. In particular, the author examines the existence, uniqueness, comparison, convergence, and stability of strong solutions to cases where the RSDE has discontinuous coefficients-with greater than linear growth-that may include jump reflection. He derives the nonlinear filtering and Zakai equations, the Maximum Principle for stochastic optimal control, and the necessary and sufficient conditions for the existence of optimal control. Most of the material presented in this book is new, including much new work by the author concerning SDEs both with and without reflection. Much of it appears here for the first time. With the application of RSDEs to various real-life problems, such as the stochastic population and neurophysiological control problems-both addressed in the text-scientists dealing with stochastic dynamic systems will find this an interesting and useful work.

Author: Eckhard Platen
Publisher: Springer Science & Business Media
ISBN: 364213694X
Category : Mathematics
Languages : en
Pages : 868

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Book Description
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 solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Author: Martin Büttner
Publisher: GRIN Verlag
ISBN: 3668233063
Category : Mathematics
Languages : en
Pages : 77

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Book Description
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.