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Polynomial Preserving Diffusions and Applications in Finance

Author

Listed:
  • Damir FILIPOVIC

    (EPFL and Swiss Finance Institute)

  • Martin LARSSON

    (EPFL)

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.

Suggested Citation

  • Damir FILIPOVIC & Martin LARSSON, 2014. "Polynomial Preserving Diffusions and Applications in Finance," Swiss Finance Institute Research Paper Series 14-54, Swiss Finance Institute, revised Dec 2015.
    • Handle: RePEc:chf:rpseri:rp1454
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    File URL: http://ssrn.com/abstract=2479826
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    Cited by:

    1. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
    2. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.

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