A NONLINEAR PARTIAL INTEGRO-DIFFERENTIAL EQUATION FROM MATHEMATICAL FINANCE

被引：31

作者：

Abergel, Frederic ^{[1
]}

Tachet, Remi ^{[1
]}

机构：

[1] Grande Voie Vignes, F-92295 Chatenay Malabry, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 27卷 / 03期

关键词：

Analysis of pde's; nonlinear parabolic partial integro-differential equation; short-time existence; fixed point methods; local and stochastic volatility models; calibration of vanillas;

D O I：

10.3934/dcds.2010.27.907

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consistently fitting vanilla option surfaces is an important issue when it comes to modeling in finance. As far as local and stochastic volatility models are concerned, this problem boils down to the resolution of a nonlinear integro-differential pde. The non-locality of this equation stems from the quotient of two integral terms and is not defined for all bounded continuous functions. In this paper, we use a fixed point argument and suitable a priori estimates to prove short-time existence of solutions for this equation.

引用

页码：907 / 917

页数：11

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