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 via probably the most exclusive researchers and practitioners within the fields of mathematical finance and fiscal engineering. featuring cutting-edge 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 strategy 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 rate 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, ok. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou

Show description

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

This self-contained quantity brings jointly a set of chapters via probably the most exclusive researchers and practitioners within the fields of mathematical finance and fiscal engineering. featuring cutting-edge 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 strategy 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 rate 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, ok. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou

Show description

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Sample text

F. f. generalizing (18) is also given. However, the fact that the skewed VG process is a difference of two independent gamma processes is still a key player in that exposition, even though the processes are no longer identically distributed. K. I believe [10] also took much too long to find a publisher. It now enjoys a well-deserved status. The photograph shown in Figure 1 taken in my Sydney office shows Dilip and me finalizing a first revision of what became [21] just before he left Sydney for the University of Maryland, and so dates to about July 1988.

167] verbatim, indicates that the deeper quantitative structure of the VG stochastic process in continuous time had already been explored in preparation for [21]: We observe . . that the shares with low β’s . . g. being 3+(3v/m2 ), . .. p. model are suggestive of the most appropriate model being a pure jump process. g. model can be shown to be a pure jump process while the process of independent stable increments has both continuous and jump components. Judging on the basis of the chi-squared statistics, it would appear that the stable model generally overstates the longtailedness.

The former depends on the first fundamental theorem of asset pricing: the existence of a martingale measure so that the price can be expressed as the expectation of an appropriately discounted payoff function. For exotic, hybrid, and complicated path-dependent derivatives, however, simulation is often the only method available. Of course, Dilip’s main research interests do not lie in simulation, but he is a regular consumer of the method, and as a result, we collaborated on two papers in the area, on control variates for pricing continuous arithmetic Asian options [12] and on pricing American-style options [11].

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