LAUSR

The distribution of the returns of an asset is still an open problem despite the variety of models and methods devised to deal with it. In this note we propose a model-free, nonparametric method for the estimation of asset returns, which is applicable also to a wider set of similar problems. The Laplace transform of a shifted rate of return or other percent change of a positive random variables can be transformed into a fractional moment problem which can then be solved by the method of maximum entropy. This is a very robust method and requires only a few values of the Laplace transform to provide good reconstructions. This method can be applied in multiple fields where model-free density estimation of functionals like percent changes of random variables is of interest.