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Polynomial diffusions and applications in finance

Damir Filipović and Martin Larsson ()
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Damir Filipović: EPFL and Swiss Finance Institute
Martin Larsson: ETH Zurich

Finance and Stochastics, 2016, vol. 20, issue 4, 931-972

Abstract: 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; 60H30; 60J60 (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2016
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