Articlebronze2018

Polynomial jump-diffusions on the unit simplex

Christa Cuchiero · Martin Larsson · Sara Svaluto‐Ferro

17 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Mathematical and Theoretical Epidemiology and Ecology Models Stochastic processes and statistical mechanics

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.

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2003Limit Theorems for Stochastic Processes 2009Mathematical Methods for Financial Markets 2010Mathematical Methods for Financial Markets 2002Stochastic Portfolio Theory 2012The Term Structure of Interbank Risk 2002Stochastic Portfolio Theory 2009Stochastic Portfolio Theory: an Overview 2012Polynomial processes and their applications to mathematical finance

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