Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit simplex under natural structural hypotheses on the jumps. As a stepping stone, we characterize well-posedness of the martingale problem for polynomial operators on general compact state spaces.

Polynomial jump-diffusions on the unit simplex

Christa Cuchiero;Sara Svaluto-Ferro
2018

Abstract

Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit simplex under natural structural hypotheses on the jumps. As a stepping stone, we characterize well-posedness of the martingale problem for polynomial operators on general compact state spaces.
Polynomial processes
stochastic invariance
stochastic models with jumps
unit simplex
Wright–Fisher diffusion
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/1051760
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