By Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott
This self-contained quantity brings jointly a set of chapters through one of the most special researchers and practitioners within the fields of mathematical finance and monetary engineering. offering state of the art advancements in thought and perform, the Festschrift is devoted to Dilip B. Madan at the social gathering of his sixtieth birthday.
Specific subject matters lined include:
* conception 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 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 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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Extra info for Advances in Mathematical Finance
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. Z. Wahrscheinlichkeutstheorie verw. Geb, 10:212–225,1968. 30. A. Tjetjep and E. Seneta. Skewed normal variance-mean models for asset pricing and the method of moments.
Loop from k = 1 to M : n ← 2M −k ; Loop from j = 1 to 2k−1 : 1. i ← (2j − 1)n; 2. Generate Yi+ , Yi− ∼ β((ti − ti−n )/ν, (ti+n − ti )/ν) independently; 3. γt+i = γt+i−n + [γt+i+n − γt+i−n ]Yi+ , γt−i = γt−i−n + [γt−i+n − γt+i−n ]Yi− ; 4. Return Xti = γt+i − γt−i . Fig. 2. Algorithms for simulating VG process on [0, T ] via bridge sampling. ; also β(1, 1) = U (0, 1). If either of the parameters is equal to 1, then the inverse transform method can be easily applied. Otherwise, the main methods to generate variates are acceptance–rejection, numerical inversion, or a special algorithm using the following known relationship with the gamma distribution: if Yi ∼ Γ (αi , ψ) independently generated, then Y1 /(Y1 +Y2 ) ∼ β(α1 , α2 ).
F. of the VG distribution. f. of the t distribution was not known. It may be interesting to Dilip and other readers if I break in the technical history of our collaboration to reﬂect on background concerning Praetz and myself. 5 The Praetz Conﬂuence The VG distribution is a direct competitor to the Praetz t, and is in fact dual to it [28, Section 6]; . Our paper  was deliberately published in the same journal. Praetz was an Australian econometrician, and focused on Sydney Stock Exchange data, as did all our collaborative papers on the VG before .
Advances in Mathematical Finance by Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott