Pricing futures by deterministic methods

Acta Numerica ◽  
2012 ◽  
Vol 21 ◽  
pp. 577-671
Author(s):  
Olivier Pironneau
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Narrow Range ◽  
Numerical Algorithms ◽  
The Other ◽  
Financial Mathematics ◽  
Pragmatic Approach ◽  
Partial Differential ◽  
Deterministic Methods ◽  
Better Than

In this article we will focus on only a small part of financial mathematics, namely the use of partial differential equations for pricing futures. Even within this narrow range it is hard to be systematic and complete, or even to do better than existing books such as Wilmott, Howison and Dewynne (1995), Achdou and Pironneau (2005), or software manuals such as Lapeyre, Martini and Sulem (2010). So this article may be valuable only to the extent that it reflects ten years of teaching, conferences and interaction with the protagonists of financial mathematics.Also, because the theory of partial differential equations is not always well known, we have chosen a pragmatic approach and left out the details of the theory or the proofs of some results, and refer the reader to other books. The numerical algorithms, on the other hand, are given in detail.

Numerical and Experimental Analysis of the Nonlinear Dynamics due to Impacts of a Continuous Overhung Rotor

1997 ◽  
Author(s):  
Mohammed F. Abdul Azeez ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Experiments ◽  
The Other ◽  
Experimental Setup ◽  
Partial Differential ◽  
Qualitative Comparison ◽  
Set Up ◽  
Theory And Experiments

Abstract This work is aimed at obtaining the transient response of an overhung rotor when there are impacts occurring in the system. An overhung rotor clamped on one end, with a flywheel on the other and impacts occurring in between, due to a bearing with clearance, is considered. The system is modeled as a continuous rotor system and the governing partial differential equations are set up and solved. The method of assumed modes is used to discretize the system in order to solve the partial differential equations. Using this method numerical experiments are run and a few of the results are presented. The different numerical issues involved are also discussed. An experimental setup was built to run experiments and validate the results. Preliminary experimental observations are presented to show qualitative comparison of theory and experiments.

Soliton Kernels for Solving PDEs

2016 ◽  
Vol 13 (02) ◽  
pp. 1640009 ◽  
Author(s):  
Marjan Uddin ◽  
H. U. Jan ◽  
Amjad Ali ◽  
I. A. Shah
Keyword(s):  
Image Processing ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Response Surface ◽  
Computer Experiments ◽  
Time Dependent ◽  
Response Surface Modeling ◽  
Partial Differential ◽  
Special Solutions ◽  
Better Than

There are many important applications in the fields of computer experiments, response surface modeling, finance and image processing, where some special types of nonstandard kernels performed better than standard kernels. These kernels are more appropriate than standard kernels when looking at special solutions of partial differential equations (PDEs). For example some nonlinear time-dependent PDEs have soliton like solutions, so soliton kernels would more suit to approximate the solution. In this work, we recover the solution of equal width equation using soliton kernels.

Interior Estimates for Elliptic Partial Differential Equations in the ℒ(q,λ) Spaces of Strong Type

1984 ◽  
Vol 36 (3) ◽  
pp. 385-404
Author(s):  
Akira Ono
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Partial Differential Equations ◽  
The Other ◽  
Usual Sense ◽  
Elliptic Type ◽  
Strong Type ◽  
Partial Differential ◽  
Interior Estimates ◽  
Isomorphism Theorems

Recently the ℒ(q,λ) spaces have been investigated by many authors and the theory of these spaces has proved to be particularly important for research in partial differential equations (see for example [15], [16] and [18]).The equations of elliptic type in these spaces were first studied by C. B. Morrey [8], [9], who applied his well-known imbedding theorems, and afterwards by S. Campanato [3], [4] with the aid of isomorphism theorems and the so-called fundamental inequalities due to him.On the other hand, G. Stampacchia introduced the ℒ(q,λ) spaces of strong type [17], the structures of which are more general and complicated than those of ℒ(q,λ) Spaces in the usual sense, and greater part of them were characterized by him, L. C. Piccinini, Y. Furusho, the author and others (see [5], [11]-[14], [16] and [17]).

Adding police to a mathematical model of burglary

2010 ◽  
Vol 21 (4-5) ◽  
pp. 401-419 ◽  
Author(s):  
ASHLEY B. PITCHER
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Continuum Limit ◽  
The Other ◽  
Residential Burglary ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
The Continuum

We review the Short model of urban residential burglary derived from taking the continuum limit of two difference equations – one of which models the attractiveness of individual houses to burglary, and the other of which models burglar movement. This leads to a system of non-linear partial differential equations. We propose a change to the Short model and also add deterrence caused by the presence of uniformed officers to the model. We solve the resulting system of non-linear partial differential equations numerically and present results both with and without deterrence.

On Partial Differential Equations in a Field of Prime Characteristic

1955 ◽  
Vol 7 ◽  
pp. 539-542 ◽  
Author(s):  
Arno Jaeger
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Prime Number ◽  
The Other ◽  
Prime Characteristic ◽  
Classical Analysis ◽  
Partial Differential ◽  
Other Hand ◽  
Algebraic Theories

In classical analysis ordinary differential equations and partial differential equations are distinct concepts, and the transition from one derivation to several partial derivations changes some of their properties distinctly. On the other hand, the algebraic theories of modified ordinary and partial differential equations (5; 6), based on the differentiations in the sense of Hasse (2) and Schmidt (3) and the multidifferentiations in the sense of Jaeger (4), turn out to be strikingly similar in the case of fields of prime number characteristic.

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