Polynomial Diffusions and Applications in Finance
43 Pages Posted: 15 Aug 2014 Last revised: 14 Mar 2016
Date Written: March 13, 2016
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
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