Polynomial diffusions and applications in finance

• Published in: Finance and stochastics Vol. 20; no. 4; pp. 931 - 972
• Main Authors: Filipović, Damir, Larsson, Martin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2016; Springer Nature B.V
• Subjects: Algebra; Commodities; Credit risk; Diffusion; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Electric rates; Electricity; Finance; Financial market; Geometry; Insurance; Interest rates; Management; Mathematics; Mathematics and Statistics; Polynomials; Probability Theory and Stochastic Processes; Quantitative Finance; Statistics for Business; Uniqueness; Volatility; Polynomial diffusions; 60H30; Boundary attainment; 60J60; G13; Moment problem; G12; Polynomial diffusion models in finance; Stochastic invariance
• ISSN: 0949-2984; 1432-1122
• DOI: 10.1007/s00780-016-0304-4

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.