By Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott
This self-contained quantity brings jointly a suite of chapters through the most individual researchers and practitioners within the fields of mathematical finance and monetary engineering. offering cutting-edge advancements in conception and perform, the Festschrift is devoted to Dilip B. Madan at the party of his sixtieth birthday.
Specific themes coated include:
* thought and alertness of the Variance-Gamma process
* Lévy method pushed fixed-income and credit-risk versions, 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 cost bubbles
* application valuation for credits derivatives and portfolio management
Advances in Mathematical Finance is a worthy 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 info for Advances in Mathematical Finance
J. Appl. , 36: 1234–1239, 1999. 9. S. Kullback. The distribution laws of the diﬀerence and quotient of variables independently distributed in Pearson type III laws. Ann. 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.
Lancaster, another leader in that area who was at the University of Sydney, and at the time editor of the Australian Journal of Statistics, which Lancaster had founded. It is possible Darroch refereed . In any case, the contact mentioned by Praetz in 1972 took place on Darroch’s return to Adelaide. Regrettably in retrospect, I never had any contact with Praetz. f. of X, where X|V ∼ N (μ, V ), where V has inverse gamma distribution described by (10), with its Bayesian and decision-theoretic interpretation, leading to a t distribution, which is of fundamental importance in elementary statistical inference theory and practice, has strong resonance with my memory of John Darroch’s teaching, and Hogg and Craig’s book.
Of X are given by ∞ F (x) = λn e−λ Φ n! n=0 x−μ θ + σ2 n , 2 φX (u) = exp iμu − u2 θ/2 + λ(e−u (5) σ2 /2 − 1) . f. 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.