Bogdan Grechuk

Learn More
An approach to the Shannon and Rényi entropy maximization problems with constraints on the mean and law invariant deviation measure for a random variable has been developed. The approach is based on the representation of law invariant deviation measures through corresponding convex compact sets of nonnegative concave functions. A solution to the problem has(More)
Mean-deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the(More)
A Markowitz-type portfolio selection problem is to minimize a deviation measure of portfolio rate of return subject to constraints on portfolio budget and on desired expected return. In this context, the inverse portfolio problem is finding a deviation measure by observing the optimal mean-deviation portfolio that an investor holds. Necessary and sufficient(More)
A linear programming SSD-efficiency test capable of identifying a dominating portfolio is proposed. It has T + n variables and at most 2T + 1 constraints, whereas the existing SSD-efficiency tests are either unable to identify a dominating portfolio, or require solving a linear program with at least O(T 2+n) variables and/or constraints.
In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the(More)
The consistency of law invariant general deviation measures, introduced by Rockafellar et al., with concave ordering has been used to generalize Rao-Blackwell theorem and to develop an approach for reducing minimization of law invariant deviation measures to minimization of the measures on subsets of undominated random variables with respect to concave(More)
Cooperative investment consists of two problems: finding an optimal cooperative investment strategy and fairly dividing investment outcome among participating agents. In general, the two problems cannot be solved separately. It is known that when agents’ preferences are represented by mean-deviation functionals, sharing of optimal portfolio creates(More)
Calculation of exceedance probabilities or the inverse problem of finding the level corresponding to a given exceedance probability occurs in many practical applications. For instance, it is often of interest in offshore engineering to evaluate the wind, wave, current, and sea ice properties with annual exceedance probabilities of, e.g., 10-1, 10-2, and(More)