Vladislav Kargin

Vladislav Kargin

We study the variation of word frequencies in Russian literary texts. Our findings indicate that the standard deviation of a word's frequency across texts depends on its average frequency according to a power law with exponent $0.62,$ showing that the rarer words have a relatively larger degree of frequency volatility (i.e., "burstiness"). Several latent factors models have been estimated to investigate the structure of the word frequency distribution. The dependence of a word's frequency volatility on its average frequency can be explained by the asymmetry in the distribution of latent factors.

Vladislav Kargin

If pricing kernels are assumed non-negative then the inverse problem of finding the pricing kernel is well-posed. The constrained least squares method provides a consistent estimate of the pricing kernel. When the data are limited, a new method is suggested: relaxed maximization of the relative entropy. This estimator is also consistent. Keywords: $ε$-entropy, non-parametric estimation, pricing kernel, inverse problems.