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001452061 001__ 1452061
001452061 003__ OCoLC
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001452061 019__ $$a1357016650
001452061 020__ $$a9783662658277$$q(electronic bk.)
001452061 020__ $$a3662658275$$q(electronic bk.)
001452061 020__ $$z9783662658260
001452061 020__ $$z3662658267
001452061 0247_ $$a10.1007/978-3-662-65827-7$$2doi
001452061 035__ $$aSP(OCoLC)1356945109
001452061 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCQ$$dUKAHL
001452061 049__ $$aISEA
001452061 050_4 $$aQA276
001452061 08204 $$a519.5$$223/eng/20230119
001452061 1001_ $$aRatanov, Nikita,$$eauthor.
001452061 24510 $$aTelegraph processes and option pricing /$$cNikita Ratanov, Alexander D. Kolesnik.
001452061 250__ $$aSecond edition.
001452061 264_1 $$aBerlin :$$bSpringer,$$c[2022]
001452061 264_4 $$c©2022
001452061 300__ $$a1 online resource (xv, 440 pages) :$$billustrations (chiefly color)
001452061 336__ $$atext$$btxt$$2rdacontent
001452061 337__ $$acomputer$$bc$$2rdamedia
001452061 338__ $$aonline resource$$bcr$$2rdacarrier
001452061 504__ $$aIncludes bibliographical references and index.
001452061 5050_ $$aIntro -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- About the Authors -- 1 Preliminaries -- 1.1 Hypergeometric Functions -- 1.2 Modified Bessel Functions -- 1.3 Generalised Functions and Integral Transforms -- 1.4 One-Dimensional Markov Processes -- 1.5 Brownian Motion and Diffusion on ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R) /StPNE pdfmark [/StBMC pdfmarkRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 1.6 Stochastic Integrals and Itô's Formula -- 1.7 Poisson Process, Exponential, and HypoexponentialDistributions
001452061 5058_ $$a2 Symmetric Telegraph Process on the Line -- 2.1 Definition of Process and the Structure of Distribution -- 2.2 Kolmogorov Equations -- 2.3 Telegraph Equation -- 2.4 Characteristic Function -- 2.5 Transition Density -- 2.6 Probability Distribution Function -- 2.7 Convergence to Brownian Motion -- 2.8 Laplace Transforms -- Notes -- 3 Asymmetric Jump-Telegraph Processes -- 3.1 Asymmetric Continuous Telegraph Process -- 3.1.1 Generator and Transition Densities -- 3.1.2 Moment Generating Functions -- 3.1.3 Moments -- 3.2 Self-Exciting Piecewise Linear Continuous Processes
001452061 5058_ $$a3.2.1 Piecewise Constant Process -- 3.2.2 Piecewise Linear Process -- 3.2.3 First Passage Time -- 3.3 Telegraph Processes with Alternating Deterministic Jumps -- 3.3.1 Transition Densities -- 3.3.2 Expectations and Variances, Jump-TelegraphMartingales -- 3.3.3 Change of Measure for Jump-Telegraph Processes -- 3.4 Telegraph Processes with Alternating Random Jumps -- 3.5 Short Memory Telegraph Processes with Random Jumps -- 3.5.1 Jump-Telegraph Processes with Parameters Depending on the Past -- 3.5.2 Martingales -- 3.6 Piecewise Linear Process with Renewal Starting Points
001452061 5058_ $$a3.6.1 Distributions of X(t) -- 3.6.2 First Passage Time -- 3.6.2.1 Positive Velocities -- 3.6.2.2 Velocities of Opposite Signs -- 3.7 Double Telegraph Processes -- 3.7.1 Doubly Stochastic Poisson Process -- 3.7.2 Doubly Stochastic Telegraph Process with Jumps -- 3.7.3 Girsanov Transformation -- 3.8 Jump-Telegraph Processes with Poisson-Modulated Exponential Switching Times -- 3.8.1 Building a Model -- 3.8.2 Poisson-Modulated Exponential Distribution -- 3.8.3 Example: Poisson-Modulated Exponential Distributions with Linearly Increasing Switching Intensities
001452061 5058_ $$a3.8.4 Piecewise Linear Process with Two Alternating Poisson Modulated Patterns and a Double Jump Component -- 3.9 Piecewise Deterministic Processes Following Two Alternating Patterns -- 3.9.1 Piecewise Linear Processes in the Linear NormedSpace -- 3.9.2 Time-Homogeneous Piecewise Deterministic Process -- 3.9.3 Examples -- 3.9.3.1 Squared Telegraph Process -- 3.9.3.2 A Random Motion in a Plane and Polar Coordinates -- 3.9.4 Self-Similarity -- 4 Jump-Diffusion Processes with Regime Switching -- 4.1 The Basic Model: Markov Modulated Jump-DiffusionProcesses
001452061 506__ $$aAccess limited to authorized users.
001452061 520__ $$aThis book provides an extensive, systematic overview of the modern theory of telegraph processes and their multidimensional counterparts, together with numerous fruitful applications in financial modelling. Focusing on stochastic processes of bounded variation instead of classical diffusion, or more generally, Levy processes, has two obvious benefits. First, the mathematical technique is much simpler, which helps to concentrate on the key problems of stochastic analysis and applications, including financial market modelling. Second, this approach overcomes some shortcomings of the (parabolic) nature of classical diffusions that contradict physical intuition, such as infinite propagation velocity and infinite total variation of paths. In this second edition, some sections of the previous text are included without any changes, while most others have been expanded and significantly revised. These are supplemented by predominantly new results concerning piecewise linear processes with arbitrary sequences of velocities, jump amplitudes, and switching intensities. The chapter on functionals of the telegraph process has been significantly expanded by adding sections on exponential functionals, telegraph meanders and running extrema, the times of the first passages of telegraph processes with alternating random jumps, and distribution of the Euclidean distance between two independent telegraph processes. A new chapter on the multidimensional counterparts of the telegraph processes is also included. The book is intended for graduate students in mathematics, probability, statistics and quantitative finance, and for researchers working at academic institutions, in industry and engineering. It can also be used by university lecturers and professionals in various applied areas.
001452061 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed January 19, 2023).
001452061 650_0 $$aStochastic analysis.
001452061 650_0 $$aOptions (Finance)
001452061 655_0 $$aElectronic books.
001452061 7001_ $$aKolesnik, Alexander D.,$$eauthor.
001452061 77608 $$iPrint version: $$z3662658267$$z9783662658260$$w(OCoLC)1333620446
001452061 852__ $$bebk
001452061 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-662-65827-7$$zOnline Access$$91397441.1
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001452061 980__ $$aBIB
001452061 980__ $$aEBOOK
001452061 982__ $$aEbook
001452061 983__ $$aOnline
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