By Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott
This self-contained quantity brings jointly a suite of chapters via the most special researchers and practitioners within the fields of mathematical finance and fiscal engineering. featuring cutting-edge advancements in idea and perform, the Festschrift is devoted to Dilip B. Madan at the celebration of his sixtieth birthday.
Specific issues lined include:
* idea 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 rate bubbles
* application valuation for credits derivatives and portfolio management
Advances in Mathematical Finance is a necessary 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, okay. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou
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Extra resources for Advances in Mathematical Finance
F. of the normal (the case β = 2). s, apart from allowing for the shift to μ, were consequently real-valued, and of simple closed form. Like the NCP, the process of independent stable increments has both continuous and jump components. d. increments with stable law also has the advantage of having laws of the same form for an increment over a time interval of any length, and heavy tails, but such laws have inﬁnite variance. The data for the statistical analysis consisted of ﬁve series of share prices and six series on economic variables.
Using a χ2 statistic for goodness of ﬁt, he concludes that the scaled t distribution gives superior ﬁt in all cases. The compound events model causes larger χ2 values through inability as in the past to provide suitable estimates of the parameters. , ν = 1, ν → ∞). These various issues served as stimulus for the creation of the VG distribution and empirical characteristic function estimation methods in  and . f. s, and persisted with this. f. f. f. corresponding to t. f. of X, where X|V ∼ N (0, 1/V ), so that in eﬀect X|V ∼ N (0, V ), where V has an ordinary gamma distribution.
Manuscript, 2006. 22. L. McLeish. A robust alternative to the normal distribution. Canadian Journal of Statistics, 10:89–102, 1982. 34 Michael C. Fu 23. L. McLeish, Monte Carlo Simulation and Finance. Wiley, 2005. 24. P. Protter. Stochastic Integration and Diﬀerential Equations, 2nd edition. Springer-Verlag, 2005. 25. C. Ribeiro, and N. Webber. Valuing path-dependent options in the VarianceGamma model by Monte Carlo with a gamma bridge. Journal of Computational Finance, 7:81–100, 2004. 26. K. Sato.