Statistical Skorohod embedding problem and its generalizations

Denis Belomestny; John Schoenmakers

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arXiv · 1407.0873

Statistical Skorohod embedding problem and its generalizations

Denis Belomestny·John Schoenmakers

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Abstract

Given a Lévy process $L$, we consider the so-called statistical Skorohod embedding problem of recovering the distribution of an independent random time $T$ based on i.i.d. sample from $L_{T}.$ Our approach is based on the genuine use of the Mellin and Laplace transforms. We propose a consistent estimator for the density of $T,$ derive its convergence rates and prove their optimality. It turns out that the convergence rates heavily depend on the decay of the Mellin transform of $T.$ We also consider the application of our results to the problem of statistical inference for variance-mean mixture models and for time-changed Lévy processes.

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Denis Belomestny, John Schoenmakers. 2014-07-03. Statistical Skorohod embedding problem and its generalizations. https://arxiv.org/abs/1407.0873

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