A characterization of the martingale property of exponentially affine processes
Eberhard Mayerhofer, Johannes Muhle-Karbe, Alexander G. Smirnov
TL;DR
This paper provides deterministic criteria based on process parameters to determine when local martingales derived from affine processes are true martingales, extending the characterization of conservative affine processes.
Contribution
It offers a complete characterization of the martingale property for exponentials of affine processes, filling a gap in the existing theory.
Findings
Deterministic necessary and sufficient conditions for martingality
Extension of the characterization of conservative affine processes
Clarification of when local martingales are true martingales
Abstract
We consider local martingales which are standard or stochastic exponentials M of one component X of a multivariate affine process in the sense of Duffie, Filipovic and Schachermayer (2003). By completing their characterization of conservative affine processes, we provide deterministic necessary and sufficient conditions in terms of the parameters of X for M to be a true martingale.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Insurance, Mortality, Demography, Risk Management