By Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott
This self-contained quantity brings jointly a suite of chapters via probably the most unique 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 social gathering of his sixtieth birthday.
Specific issues 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
* 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 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 info for Advances in Mathematical Finance
Journal of Economic Dynamics and Control, 21:1267–1321, 1997. 3. M. Broadie and P. Glasserman. Estimating security price derivatives using simulation. Management Science, 42:269–285, 1996. 4. P. Carr, H. B. Madan, and M. Yor. The ﬁne structure of asset returns: An empirical investigation. Journal of Business, 75:305–332, 2002. 5. P. Carr, H. B. Madan, and M. Yor. Stochastic volatility for L´evy processes. Mathematical Finance, 2:87–106, 2003. 6. P. Carr and D. Madan. Option valuation using the fast Fourier transform.
Madan and E. Seneta. Chebyshev polynomial approximations and characteristic function estimation. Econometric Discussion Papers, No. 87-04, 13 pp, University of Sydney, 1987. 18. B. Madan and E. Seneta. Chebyshev polynomial approximations and characteristic function estimation. R. Statist. , Ser. B, 49:163–169, 1987. 19. B. Madan and E. Seneta. Characteristic function estimation using maximum likelihood on transformed variables. Econometric Discussion Papers, No. 87-08, 9 pp, University of Sydney, 1987.
It is particularly eﬀective in combination with quasi-Monte Carlo methods, because the sampling sequence usually means that the ﬁrst samples are more critical than the latter ones, leading to a lower “eﬀective dimension” than in the usual sequential sampling. It is in this setting that quasi-Monte Carlo methods show the greatest improvement over traditional MC methods, and gamma bridge sampling coupled with quasi-Monte Carlo is treated in  and . The main idea of bridge sampling is that the conditional distribution of a stochastic process Xt at time t ∈ (T1 , T2 ), given XT1 and XT2 can be easily obtained; that is, for T1 ≤ t ≤ T2 , one can apply Bayes’ rule to get the necessary conditional distribution: P (Xt |XT1 , XT2 ) = P (XT2 |XT1 , Xt )P (Xt |XT1 ) .
Advances in Mathematical Finance by Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott