New PDF release: Advances in Mathematical Finance

By Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott

ISBN-10: 0817645446

ISBN-13: 9780817645441

ISBN-10: 0817645454

ISBN-13: 9780817645458

This self-contained quantity brings jointly a set of chapters via one of the most special researchers and practitioners within the fields of mathematical finance and fiscal engineering. featuring state of the art advancements in concept and perform, the Festschrift is devoted to Dilip B. Madan at the social gathering of his sixtieth birthday.

Specific subject matters coated include:

* concept and alertness of the Variance-Gamma process

* Lévy procedure pushed fixed-income and credit-risk types, together with CDO pricing

* Numerical PDE and Monte Carlo methods

* Asset pricing and derivatives valuation and hedging

* Itô formulation for fractional Brownian motion

* Martingale characterization of asset expense bubbles

* application valuation for credits derivatives and portfolio management

Advances in Mathematical Finance is a beneficial source for graduate scholars, researchers, and practitioners in mathematical finance and monetary engineering.

Contributors: H. Albrecher, D. C. Brody, P. Carr, E. Eberlein, R. J. Elliott, M. C. Fu, H. Geman, M. Heidari, A. Hirsa, L. P. Hughston, R. A. Jarrow, X. Jin, W. Kluge, S. A. Ladoucette, A. Macrina, D. B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, ok. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou

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Additional resources for Advances in Mathematical Finance

Example text

A sample X1 , X2 , . . d. random variables is transformed via Ti = ψ(ωXi ), i = 1, 2, . . , n, where ω > 0 is a parameter chosen at will to control the loss of information in going to the transformed sample. ), if the function ψ is an even (or odd) function, the random variable T will be symmetrically distributed on (−b/ω, b/ω]. f. depends on the same parameters as the distribution of X, if it is explicitly available, these parameters may be estimated by maximum likelihood procedures from the transformed observations T1 , T2 , .

N i=1 Δti = T . Initialization: Set X0 = 0; σε2 = +ε −ε x2 k(x)dx, λ+ ε = ∞ +ε −ε k(x)dx, λ− ε = −∞ k(x)dx, − − kε+ (x) = k(x)1{x≥ε} /λ+ ε , kε (x) = k(x)1{x≤−ε} /λε . Loop from i = 1 to N : 1. , Ni− , Xi,j Zi ∼ N (0, 1). √ 2. Return Xti = Xti−1 + Zi σε Δti + Ni+ j=1 + Xi,j + Ni− j=1 − Xi,j . Fig. 1. Algorithms for sequentially simulating VG process on [0, T ]. Variance-Gamma and Monte Carlo 27 Instead of sequential sampling, which progresses chronologically forward in time, an alternative method for simulating asset price paths is to use bridge sampling, which samples the end of the path first, and then “fills in” the rest of the path as needed.

Austral. J. , 11:123–139, 1969. 25. D. Praetz. The distribution of share price changes. J. Business, 45:49–55,1972. 26. J. Press. A compound events model for security prices. J. Business, 40:317– 335, 1967. 27. W. Schoutens. L´evy Processes in Finance: Pricing Financial Derivatives. Wiley, 2003. 28. E. Seneta. Fitting the Variance-Gamma model to financial data. C. Heyde Festschrift), eds. J. Gani and E. Seneta, J. Appl. , 41A:177–187, 2004. 29. E. Seneta and D. Vere-Jones. On the asymptotic behaviour of subcritical branching processes with continuous state-space.

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Advances in Mathematical Finance by Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott


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