2013/11/30 by Joscha Diehl, Peter Friz, Hilmar Mai · 8 citations
Economics, Econometrics and Finance · Mathematics · #Estimation theory #Estimator #Financial Risk and Volatility Modeling #Maximum likelihood #Robustness (evolution) #Stability (learning theory) #Statistical Methods and Inference #Stochastic processes and financial applications #Volatility (finance) #math.PR
paper · pdf · doi:10.1214/15-aap1143
published in The Annals of Applied Probability 26(4) (Institute of Mathematical Statistics) · Published at http://dx.doi.org/10.1214/15-AAP1143 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex created_date 2016/06/24 · openalex publication_date 2016/08/01 · arxiv created 2016/09/28 · arxiv updated 2016/09/29 · openalex updated_date 2026/08/05
We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with regard to its pathwise stability properties as well as robustness toward misspecification in volatility and even the very nature of the noise. Two numerical examples demonstrate the practical relevance of our results.