Optimal Stopping Rules
Author | : Alʹbert Nikolaevich Shiri︠a︡ev |
Publisher | : Springer |
Total Pages | : 238 |
Release | : 1978 |
Genre | : Mathematics |
ISBN | : |
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Author | : Alʹbert Nikolaevich Shiri︠a︡ev |
Publisher | : Springer |
Total Pages | : 238 |
Release | : 1978 |
Genre | : Mathematics |
ISBN | : |
Author | : Yuan Shih Chow |
Publisher | : |
Total Pages | : 168 |
Release | : 1971 |
Genre | : Mathematics |
ISBN | : |
Author | : Goran Peskir |
Publisher | : Springer Science & Business Media |
Total Pages | : 515 |
Release | : 2006-11-10 |
Genre | : Mathematics |
ISBN | : 3764373903 |
This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.
Author | : Yuan Shih Chow |
Publisher | : Dover Publications |
Total Pages | : 139 |
Release | : 1991-01 |
Genre | : Mathematics |
ISBN | : 9780486666501 |
Author | : Svetlana Boyarchenko |
Publisher | : Springer Science & Business Media |
Total Pages | : 292 |
Release | : 2007-08-26 |
Genre | : Business & Economics |
ISBN | : 3540737464 |
Here, two highly experienced authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.
Author | : Brian Christian |
Publisher | : Macmillan |
Total Pages | : 366 |
Release | : 2016-04-19 |
Genre | : Business & Economics |
ISBN | : 1627790365 |
'Algorithms to Live By' looks at the simple, precise algorithms that computers use to solve the complex 'human' problems that we face, and discovers what they can tell us about the nature and origin of the mind.
Author | : Thomas Shelburne Ferguson |
Publisher | : IMS |
Total Pages | : 302 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780940600485 |
Author | : Denis Belomestny |
Publisher | : Springer |
Total Pages | : 364 |
Release | : 2018-01-31 |
Genre | : Business & Economics |
ISBN | : 1137033517 |
This is an advanced guide to optimal stopping and control, focusing on advanced Monte Carlo simulation and its application to finance. Written for quantitative finance practitioners and researchers in academia, the book looks at the classical simulation based algorithms before introducing some of the new, cutting edge approaches under development.
Author | : Tomas Björk |
Publisher | : Springer Nature |
Total Pages | : 328 |
Release | : 2021-11-02 |
Genre | : Mathematics |
ISBN | : 3030818438 |
This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications. In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.
Author | : R. Cairoli |
Publisher | : John Wiley & Sons |
Total Pages | : 348 |
Release | : 2011-07-26 |
Genre | : Mathematics |
ISBN | : 1118164407 |
Sequential Stochastic Optimization provides mathematicians andapplied researchers with a well-developed framework in whichstochastic optimization problems can be formulated and solved.Offering much material that is either new or has never beforeappeared in book form, it lucidly presents a unified theory ofoptimal stopping and optimal sequential control of stochasticprocesses. This book has been carefully organized so that littleprior knowledge of the subject is assumed; its only prerequisitesare a standard graduate course in probability theory and somefamiliarity with discrete-parameter martingales. Major topics covered in Sequential Stochastic Optimization include: * Fundamental notions, such as essential supremum, stopping points,accessibility, martingales and supermartingales indexed by INd * Conditions which ensure the integrability of certain suprema ofpartial sums of arrays of independent random variables * The general theory of optimal stopping for processes indexed byInd * Structural properties of information flows * Sequential sampling and the theory of optimal sequential control * Multi-armed bandits, Markov chains and optimal switching betweenrandom walks