Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
356
result(s) for
"Derivative securities Mathematics."
Sort by:
Mathematical Techniques in Finance
Originally published in 2003,Mathematical Techniques in Financehas become a standard textbook for master's-level finance courses containing a significant quantitative element while also being suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cerný mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation.
The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated.
A standard textbook for graduate finance coursesIntroduction to asset pricing, portfolio selection, risk measurement, and investment evaluationDetailed examples and MATLAB codes integrated throughout the textExercises and summaries of main points conclude each chapter
eBook
Mathematical techniques in finance
Originally published in 2003, Mathematical Techniques in Finance has become a standard textbook for master's-level finance courses containing a significant quantitative element while also being suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cern mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation.
eBook
A compact finite difference scheme for solving fractional Black-Scholes option pricing model
In this work, we introduce an efficient compact finite difference (CFD) method for solving the time-fractional Black-Scholes (TFBS) option pricing model. The time-fractional derivative is described using Caputo-Fabrizio (C-F) fractional derivative, and a compact finite difference method is employed to discretize the spatial derivative. The main contribution of this work is to develop a high-order discrete scheme for the TFBS model. In the numerical scheme, we have developed a convergence rate of
O
(
τ
2
+
h
4
)
, where
τ
denotes the temporal step and
h
represents the spatial step. To verify the effectiveness of the proposed method, we have conducted stability analysis and error estimation using the Fourier method. Furthermore, a series of numerical experiments were conducted, and the numerical results demonstrated the theoretical order of accuracy and illustrated the effectiveness of the proposed method.
Journal Article
An H2N2 Interpolation for Caputo Derivative with Order in (1, 2) and Its Application to Time-Fractional Wave Equations in More Than One Space Dimension
In this paper, a new derived method is developed for a known numerical differential formula of the Caputo fractional derivative of order
γ
∈
(
1
,
2
)
(Li and Zeng in Numerical methods for fractional calculus. Chapman & Hall/CRC numerical analysis and scientific computing, CRC Press, Boca Raton, 2015) by means of the quadratic interpolation polynomials, and a concise expression of the truncation error is given. This new method will be called as the H2N2 method because of the application of the quadratic Hermite and Newton interpolation polynomials. A finite difference scheme with a second order accuracy in space and a
(
3
-
γ
)
-th order accuracy in time based on the H2N2 method is constructed for the initial boundary value problem of time-fractional wave equations. The stability and convergence of the difference scheme are proved. Furthermore, in order to increase computational efficiency, using the sum-of-exponentials to approximate the kernel
t
1
-
γ
, a fast difference scheme is presented. The problem with weak regularity at the initial time is also discussed with the help of the graded meshes. At each time level, the difference scheme is solved with a fast Poisson solver. Numerical results show the effectiveness of the two difference schemes and confirm our theoretical analysis.
Journal Article
Computing B-Stationary Points of Nonsmooth DC Programs
Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc) minimization problem. The contributions of this paper are (i) clarify several kinds of stationary solutions and their relations; (ii) develop and establish the convergence of a novel algorithm for computing a d-stationary solution of a problem with a convex feasible set that is arguably the sharpest kind among the various stationary solutions; (iii) extend the algorithm in several directions including a randomized choice of the subproblems that could help the practical convergence of the algorithm, a distributed penalty approach for problems whose objective functions are sums of dc functions, and problems with a specially structured (nonconvex) dc constraint. For the latter class of problems, a pointwise Slater constraint qualification is introduced that facilitates the verification and computation of a B(ouligand)-stationary point.
Journal Article