Polynomial jump-diffusions on the unit simplex

TL;DR

This paper fully characterizes polynomial jump-diffusions on the unit simplex, providing a comprehensive parameterization under natural conditions, and explores well-posedness of related martingale problems for compact spaces.

Contribution

It offers a complete parameterization of polynomial jump-diffusions on the unit simplex and characterizes martingale problem well-posedness on compact spaces.

Findings

Full parameterization of polynomial jump-diffusions on the unit simplex

Characterization of martingale problem well-posedness for polynomial operators

Applicability to finance and population genetics

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.