arXiv subjects

Valentyn Khokhlov

Publications and source records attributed to Valentyn Khokhlov.

4 recordsLinked to original sources

arXiv2026

Necessary and Sufficient Conditions for Proving Choice in Zermelo-Fraenkel Set Theory

This paper introduces an alternative approach to proving the existence of choice functions for specific families of sets within Zermelo-Fraenkel set theory (ZF) without assuming any form on the Axiom of Choice (AC). Traditional methods of proving choice, when it is possible without AC, are based on explicit constructing a choice function, which relies on being able to identify canonical elements within the sets. Our approach, instead, employs the axiom schema of separation. We begin by considering families of well-ordered sets, then apply the schema of separation twice to build a set of possible candidates for the choice functions, and, finally, prove that this set is non-empty. This strategy enables proving the existence of choice function in situations where canonical elements cannot be identified explicitly. We then extend our method beyond families of well-ordered sets to families of sets, over which partial orders with a least element exist. After exploring possibilities for further generalization, we establish a necessary and sufficient condition: in ZF, without assuming AC, a choice function exists for a non-empty family if and only if each set admits a partial order with a least element. Finally, we demonstrate how this approach can be used to prove the existence of choice functions for families of contractible and path-connected topological spaces, including hyper-intervals in $\mathbb{R}^n$, hyper-balls, and hyper-spheres.

math.LO↗

arXiv2026

Multi-period Newsvendor Model

The newsvendor model is a well-known stochastic model for inventory management; however, it was originally developed for a single-period context and focuses on trading companies. This paper proposes an extension of the newsvendor model into a mutli-period setting, aiming to develop a decision-making tool for manufacturing firms to determine the optimal production batch size. The objective function is to maximize operating profit in accordance with generally accepted accounting principles. The model can also incorporate overhead costs, such as warehousing, shrinkage, cost of capital, and lead time between the production decision and output. Monte Carlo simulations demonstrate that the proposed model results in higher profitability compared to other newsvendor models used in our analysis, as well as the safety stock buffer approach. The key feature explaining its outperformance is better adaptability of the production batch size, that leads to fewer stock-outs relative to other newsvendor models and lower inventory levels compared to the safety stock buffer approach. The robustness analysis shows that the proposed model is quite tolerant of mismatches between the "model" and the "true" demand distributions. Finally, we provide some recommendations on selecting the appropriate "model" distribution for different SKUs.

math.OC↗

arXiv2021

Conditional Value at Risk and Partial Moments for the Metalog Distributions

The metalog distributions represent a convenient way to approach many practical applications. Their distinctive feature is simple closed-form expressions for quantile functions. This paper contributes to further development of the metalog distributions by deriving the closed-form expressions for the Conditional Value at Risk, a risk measure that is closely related to the tail conditional expectations. It also addressed the derivation of the first-order partial moments and shows that they are convex with respect to the vector of the metalog distribution parameters.

q-fin.RM↗

arXiv2019

Calculating CVaR and bPOE for Common Probability Distributions With Application to Portfolio Optimization and Density Estimation

Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR), also called the superquantile and quantile, are frequently used to characterize the tails of probability distribution's and are popular measures of risk. Buffered Probability of Exceedance (bPOE) is a recently introduced characterization of the tail which is the inverse of CVaR, much like the CDF is the inverse of the quantile. These quantities can prove very useful as the basis for a variety of risk-averse parametric engineering approaches. Their use, however, is often made difficult by the lack of well-known closed-form equations for calculating these quantities for commonly used probability distribution's. In this paper, we derive formulas for the superquantile and bPOE for a variety of common univariate probability distribution's. Besides providing a useful collection within a single reference, we use these formulas to incorporate the superquantile and bPOE into parametric procedures. In particular, we consider two: portfolio optimization and density estimation. First, when portfolio returns are assumed to follow particular distribution families, we show that finding the optimal portfolio via minimization of bPOE has advantages over superquantile minimization. We show that, given a fixed threshold, a single portfolio is the minimal bPOE portfolio for an entire class of distribution's simultaneously. Second, we apply our formulas to parametric density estimation and propose the method of superquantile's (MOS), a simple variation of the method of moment's (MM) where moment's are replaced by superquantile's at different confidence levels. With the freedom to select various combinations of confidence levels, MOS allows the user to focus the fitting procedure on different portions of the distribution, such as the tail when fitting heavy-tailed asymmetric data.

q-fin.RM↗