- Working Paper
This article 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 diffusions on nonnegativity sets of C 2 functions. In conjunction with tools from real algebraic geometry this yields existence and detailed boundary attainment conditions for polynomial preserving diffusions on semialgebraic sets. Several particular semialgebraic state spaces are analyzed in detail, including the unit ball, the product of the unit cube and nonnegative orthant, as well as the unit simplex Show more
Journal / seriesarXiv
Organisational unit09546 - Larsson, Martin
NotesSubmitted 3 April 2014, Last revised 11 August 2014.
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