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OverviewThe book discusses a class of discrete time stochastic growth processes for which the growth rate is proportional to the exponential of a Gaussian Markov process. These growth processes appear naturally in problems of mathematical finance as discrete time approximations of stochastic volatility models and stochastic interest rates models such as the Black-Derman-Toy and Black-Karasinski models. These processes can be mapped to interacting one-dimensional lattice gases with long-range interactions. The book gives a detailed discussion of these statistical mechanics models, including new results not available in the literature, and their implication for the stochastic growth models. The statistical mechanics analogy is used to understand observed non-analytic dependence of the Lyapunov exponents of the stochastic growth processes considered, which is related to phase transitions in the lattice gas system. The theoretical results are applied to simulations of financial models and are illustrated with Mathematica code. The book includes a general introduction to exponential stochastic growth with examples from biology, population dynamics and finance. The presentation does not assume knowledge of mathematical finance. The new results on lattice gases can be read independently of the rest of the book. The book should be useful to practitioners and academics studying the simulation and application of stochastic growth models. Full Product DetailsAuthor: Dan PirjolPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2022 Weight: 0.280kg ISBN: 9783031111426ISBN 10: 3031111427 Pages: 132 Publication Date: 02 September 2022 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsChapter 1. Introduction to stochastic exponential growth.- Chapter 2. Stochastic growth processes with exponential growth rates.- Chapter 3. Lattice gas analogy.- Chapter 4. One-dimensional lattice gases with linear interaction.- Chapter 5. One-dimensional lattice gas with exponential attractive potentials.- Chapter 6. Asymptotic growth rates for exponential stochastic growth processes.- Chapter 7. Applications.ReviewsAuthor InformationDan Pirjol is working at the interface of mathematical physics, probability theory and mathematical finance. His main research interests are in applied probability, mathematical finance and statistical physics. After doing research in theoretical high energy physics he worked on financial engineering and model risk management for Merrill Lynch, Markit and JP Morgan, most recently in the Model Risk group. Since 2019 he joined the faculty of the School of Business at Stvens Institute of Technology. Tab Content 6Author Website:Countries AvailableAll regions |
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