Finance: Theory and Practice | 2026
Authors: Minasyan V.B.
DOI: 10.26794/2587-5671-2026-30-3-214-229
Journal: Finance: Theory and Practice
Year: 2026
Publisher: Financial University under The Government of Russian Federation
Document Type: Article
Open Access: All Open Access; Gold Open Access
Cited by: 0
The concept of stochastic order between random variables has been formed and developed in science since the middle of the 20th century. However, it was only in the last decade that these concepts began to penetrate into risk management applications and into the actuarial field. This has made it possible for them to become an actively developing area, allowing us to compare the risk factors themselves, as well as the level of hazards (risks) associated with them. The purpose of this work is to develop recommendations for solving the problem of comparing various risks and to propose methods for comparing risks with different degrees of catastrophicity. The relations of stochastic and dispersion orders in a set of risks are investigated. As a result, a study of these orders is carried out using risk measures VaR, as well as risk measures VaR(t ) (VaR to the power of t), introduced into scientific use in recent years. The description of these orders is analyzed using the stop loss method of risk transformation, as well as the danger rate method. In addition, in this study, for well-known examples of loss distributions are given that find wide application in risk management and actuarial science. Simple methods are obtained to allow one to compare risks under these distributions, which are expressed through the parameters of these distributions. The results and methods presented in this work may be of interest to both practitioners and researchers involved in the problems of risk management and the actuarial fields. © Minasyan V.B., 2026.
danger rate; dispersion order; risk measure VaR; risk measure VaR to the power of t; spreads VaR; stochastic order; stop loss risk transformation; VaR to the power of t