Pricing futures by deterministic methods*

IF 16.3 1区数学 Q1 MATHEMATICS

Acta Numerica Pub Date : 2012-04-19 DOI:10.1017/S0962492912000074

O. Pironneau

引用次数: 2

Abstract

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.

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期货定价的确定性方法*

在本文中，我们将只关注金融数学的一小部分，即使用偏微分方程为期货定价。即使在这个狭窄的范围内，也很难做到系统和完整，甚至很难比现有的书籍(如Wilmott, Howison和Dewynne (1995)， Achdou和Pironneau(2005))或软件手册(如Lapeyre, Martini和Sulem(2010))做得更好。因此，这篇文章可能只有在它反映了十年来的教学、会议和与金融数学的主角们的互动的程度上才有价值。此外，因为偏微分方程的理论并不总是众所周知的，我们选择了一种实用的方法，省略了理论的细节或一些结果的证明，并建议读者参阅其他书籍。另一方面，详细地给出了数值算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Numerica MATHEMATICS-

CiteScore

26.00

自引率

0.70%

发文量

期刊介绍： Acta Numerica stands as the preeminent mathematics journal, ranking highest in both Impact Factor and MCQ metrics. This annual journal features a collection of review articles that showcase survey papers authored by prominent researchers in numerical analysis, scientific computing, and computational mathematics. These papers deliver comprehensive overviews of recent advances, offering state-of-the-art techniques and analyses. Encompassing the entirety of numerical analysis, the articles are crafted in an accessible style, catering to researchers at all levels and serving as valuable teaching aids for advanced instruction. The broad subject areas covered include computational methods in linear algebra, optimization, ordinary and partial differential equations, approximation theory, stochastic analysis, nonlinear dynamical systems, as well as the application of computational techniques in science and engineering. Acta Numerica also delves into the mathematical theory underpinning numerical methods, making it a versatile and authoritative resource in the field of mathematics.