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 essentially the most exclusive researchers and practitioners within the fields of mathematical finance and monetary engineering. providing state of the art advancements in conception 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 approach 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 precious 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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Example text

34. D. Madan. Economics: Its Questions and Answers No. 37. D. Madan. A New View of Science or at Least Social Science No. 38. D. Madan. An Alternative to Econometrics in Economic Data Analyses There were also technical papers foreshadowing things to come on his return to the University of Maryland, for example: • No. 23. P. de Jong and D. Madan. The Fast Fourier Transform in Applied Spectral Inference Dilip was clearly interested in, and very capable in, an extraordinarily wide range of topics.

The ξi , i = 1, 2, . . d. N (0, σ 2 ) rv’s, probabilistically independent of the process {b(t)}. The process {Z(t), t ≥ 0}, called in [14] the Normal Compound Poisson (NCP) process, is therefore a process with independent stationary increments, whose distribution (the NCP distribution) over unit time interval, is given by: X|V ∼ N (μ, θ + σ 2 V ), where V ∼ Poisson(λ). ) 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.

F. of a transformed variable T in terms of φX (u). The transforming function ψ(·) is taken as a simple bounded periodic function of period 2π, which maps the interval [−π, π) onto the interval [−b, b), for fixed b. The transformation of the whole sample space of X to that of T is in general not one-to-one, thus involving some loss of information. A sample X1 , X2 , . . d. random variables is transformed via Ti = ψ(ωXi ), i = 1, 2, . . , n, where ω > 0 is a parameter chosen at will to control the loss of information in going to the transformed sample.

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