Applied Stochastic Processes and Control for Jump Diffusions: Modeling, Analysis, and ComputationThis self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems. The book emphasises modelling and problem solving, and presents sample applications in financial engineering and biomedical modelling. Computational and analytic exercises and examples are included throughout. While classical applied mathematics is used in most of the chapters to set up systematic derivations and essential proofs, the final chapter bridges the gap between the applied and the abstract worlds to give readers an understanding of the more abstract literature on jump diffusions. Appendices are available on the book's supplementary Web page. |
Contents
DC13_ch1 | 1 |
DC13_ch2 | 31 |
DC13_ch3 | 63 |
DC13_ch4 | 81 |
DC13_ch5 | 129 |
DC13_ch6 | 169 |
DC13_ch7 | 193 |
DC13_ch8 | 219 |
DC13_ch9 | 241 |
DC13_ch10 | 287 |
DC13_ch11 | 339 |
DC13_ch12 | 361 |
DC13_bm | 403 |
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Common terms and phrases
AP(t applications approximation assumed backward Black–Scholes boundary condition calculus chain rule Chapter compound Poisson process computational constant coefficient convergence corresponding dB(t density deterministic differential diffusion process discrete dP(t dX(t dynamic programming error expectation exponent exponential finite difference formula function given Hanson independent increments infinitesimal Itá Itó jump process jump-amplitude jump-diffusion process jump-rate jump-time Kloeden Lemma Lévy process mark Markov martingale MATLAB mean square limit measure method Monte Carlo noise normal distribution notation Online Appendix optimal control option pricing P(dt parameter Poisson distribution Poisson jump Poisson process Poisson random measure portfolio probability problem process X(t quadratic random variable sample paths satisfies simulated ſº solution stochastic chain rule stochastic diffusion stochastic integral stochastic processes t)d W(t t)dt Theorem time-dependent transformation variance vector Wiener process zero zero-one jump law