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

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

This self-contained quantity brings jointly a set of chapters by means of one of the most individual researchers and practitioners within the fields of mathematical finance and monetary engineering. proposing cutting-edge advancements in conception and perform, the Festschrift is devoted to Dilip B. Madan at the celebration of his sixtieth birthday.

Specific themes lined include:

* thought and alertness of the Variance-Gamma process

* Lévy technique 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

* software valuation for credits derivatives and portfolio management

Advances in Mathematical Finance is a worthwhile source for graduate scholars, researchers, and practitioners in mathematical finance and fiscal 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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Math. , 7:51– 53,1936. 10. B. Madan, P. C. Chang. The variance gamma process and option pricing. European Finance Review, 2:79–105, 1998. The Early Years of the Variance-Gamma Process 19 11. B. Madan and F. Milne. Option pricing with VG martingale components. Mathematical Finance, 1(4): 19–55,1991. 12. B. Madan and E. Seneta. The profitability of barrier strategies for the stock market. 45, 39 pp, University of Sydney, 1981. 13. B. Madan and E. Seneta. Residuals and the compound Poisson process.

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. L´evy Processes and Infinitely Divisible Distributions.

Of a standard normal distribution. The distribution of X is thus a normal with mixing on the variance, is symmetric about μ, and has the same form irrespective of the size of time increment t. It is long-tailed relative to the normal in the sense that its kurtosis value 3λσ 4 3+ (θ + σ 2 λ)2 exceeds that of the normal (whose kurtosis value is 3). When the NCP distribution is symmetrized about the origin by putting μ = 0, it has a simple real characteristic function of closed form. The NCP process from the structure (3) clearly has jump components (the ξi s are regarded as “shocks” arriving at Poisson rate), and through the Brownian process add-on θ1/2 b(t) in (3), has obviously a Gaussian component.

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