Polynomial Preserving Diffusions and Applications in Finance

Damir Filipovic and Martin Larsson
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Damir Filipovic: EPFL and Swiss Finance Institute
Martin Larsson: EPFL

No 14-54, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: This paper provides the mathematical foundation for polynomial preserving 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 preserving 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 Preserving Diffusions; Polynomial Diffusion Models in Finance; Martingale Problem; Stochastic Invariance; Boundary Attainment (search for similar items in EconPapers)
Pages: 42 pages
Date: 2014-08, Revised 2015-12
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1454

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