Polynomial Diffusions and Applications in Finance

43 Pages Posted: 15 Aug 2014 Last revised: 14 Mar 2016

See all articles by Damir Filipović

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Martin Larsson

ETH Zurich - Department of Mathematics

Date Written: March 13, 2016

Abstract

This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities and electricity. Uniqueness of polynomial diffusions is established via moment determinacy in combination with pathwise uniqueness. Existence boils down to a stochastic invariance problem that we solve for semialgebraic state spaces. Examples include the unit ball, the product of the unit cube and nonnegative orthant, and the unit simplex.

Keywords: Polynomial Diffusions, Polynomial Diffusion Models in Finance, Stochastic Invariance, Boundary Attainment, Moment Problem

Suggested Citation

Filipovic, Damir and Larsson, Martin, Polynomial Diffusions and Applications in Finance (March 13, 2016). Finance and Stochastics, Forthcoming; Swiss Finance Institute Research Paper No. 14-54. Available at SSRN: https://ssrn.com/abstract=2479826 or http://dx.doi.org/10.2139/ssrn.2479826

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Martin Larsson

ETH Zurich - Department of Mathematics ( email )

Ramistrasse 101
Zurich, 8092
Switzerland

HOME PAGE: http://math.ethz.ch/~larssonm

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