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Random dynamical systems in finance / Anatoliy Swishchuk and Shafiqul Islam.

By: Contributor(s): Material type: TextTextPublication details: Boca Raton : CRC Press, c2013.Description: xvii, 339 p. : illustrations ; 24 cmISBN:
  • 9781439867181 (hardcover : alk. paper)
Subject(s): DDC classification:
  • 000SB:332 23 Sw979
Contents:
1. Introduction -- 2. Deterministic dynamical systems and stochastic perturbations -- 3. Random dynamical systems and random maps -- 4. Position dependent random maps -- 5. Random evolutions as random dynamical systems -- 6. Averaging of the Geometric Markov Renewal Processes (GMRP) -- 7. Diffusion approximations of the GMRP and option price formulas -- 8. Normal deviation of a security market by the GMRP -- 9. Poisson approximation of a security market by the Geometric Markov Renewal Processes -- 10. Stochastic stability of fractional RDS in finance -- 11. Stability of RDS with jumps in interest rate theory -- 12. Stability of delayed RDS with jumps and regime-switching in finance -- 13. Optimal control of delayed RDS with applications in economics -- 14. Optimal control of vector delayed RDS with applications in finance and economics -- 15. RDS in option pricing theory with delayed/path-dependent information -- 16. Epilogue-- Index.
Summary: The book explains how the theory of RDS can describe the asymptotic and qualitative behavior of systems of random and stochastic differential/difference equations in terms of stability, invariant manifolds, and attractors. The authors present many models of RDS and develop techniques for implementing RDS as approximations to financial models and option pricing formulas. For example, they approximate geometric Markov renewal processes in ergodic, merged, double-averaged, diffusion, normal deviation, and Poisson cases and apply the obtained results to option pricing formulas.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 000SB:332 Sw979 (Browse shelf(Opens below)) Available 135501
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. Deterministic dynamical systems and stochastic perturbations --
3. Random dynamical systems and random maps --
4. Position dependent random maps --
5. Random evolutions as random dynamical systems --
6. Averaging of the Geometric Markov Renewal Processes (GMRP) --
7. Diffusion approximations of the GMRP and option price formulas --
8. Normal deviation of a security market by the GMRP --
9. Poisson approximation of a security market by the Geometric Markov Renewal Processes --
10. Stochastic stability of fractional RDS in finance --
11. Stability of RDS with jumps in interest rate theory --
12. Stability of delayed RDS with jumps and regime-switching in finance --
13. Optimal control of delayed RDS with applications in economics --
14. Optimal control of vector delayed RDS with applications in finance and economics --
15. RDS in option pricing theory with delayed/path-dependent information --
16. Epilogue--
Index.

The book explains how the theory of RDS can describe the asymptotic and qualitative behavior of systems of random and stochastic differential/difference equations in terms of stability, invariant manifolds, and attractors. The authors present many models of RDS and develop techniques for implementing RDS as approximations to financial models and option pricing formulas. For example, they approximate geometric Markov renewal processes in ergodic, merged, double-averaged, diffusion, normal deviation, and Poisson cases and apply the obtained results to option pricing formulas.

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