FINANCIAL MODELING: PROBABILITY THEORETIC APPROACHES

Background. A large number of significant socio-economic events occur under the influence of unique factors. Formal application of probabilistic and statistical methods in such cases leads to analytical conclusions without sufficient scientific justification. Financial modeling reflects modern approaches to the probability interpretation, provides introduction and systematization of risk indicators, and the necessity of improving theoretical and probabilistic disciplines of economic orientation. Analysis of recent research and publications has shown that despite significant investigations, financial modeling is not theoretically complete scientific direction in terms of economic risk indicators and derivative characteristics, important scientific and practical problems remain unresolved in the analysis of socio-economic phenomena in unce­rtainty and implementation of modern achievements of scientists to the process. The aim of the article is to study theoretical and probabilistic concepts of socio-economic processes in conditions of uncertainty and uniqueness based on the financial modeling methods. Materials and methods. Analytical and statistical methods, methods of mathematical statistics and probability theory are used in the research process. Information database is data from trading sessions of world stock markets. Results. Theoretical and probabilistic concepts, including interpretations of probability and risk are considered through formalization of the analysis process by the subject of the socio-economic phenomenon in conditions of uncertainty. Models of typical stationary, dynamic, parity and dominant lotteries with introduced risk indicators are built. Risk is interpreted as the ratio of negative and favorable factors of the phenomenon information background. Relevant indicators are illustrated and calculated using various socio-economic and financial cases. Subjective-probabilistic modeling (SPM) in relation to decision-making in the financial market is studied as the development of Bayesian subjectivism. It has been shown that group consensus SPM-assessments of risk generate specific derivative financial instruments such as binary options, index derivatives, crypto-assets, etc. Conclusion. The results of the study showed the application effectiveness of financial modeling methods of risks assessment in financial markets, the prospects of relevant development in the field of financial engineering. Teaching economic disciplines, which are based on theoretical and probabilistic postulates, statistical and analytical-statistical procedures for calculating probabilistic indicators (probability, risk, prevention regulations, etc.), requires significant addition using the introduction of new methods of information analysis of social background, financial sphere to determine the optimal direction of development and investment activities. Keywords: risk ratio, probability interpretation, binary options, financial modeling, high-risk financial markets, subjective-probabilistic modeling.

Risk assessment of COVID-19 based on a new structure of neural fuzzy probabilistic model

The risk assessment of the COVID-19 infection can save so many lives, reduce treatment costs, and increase public health. The unknown nature of the COVID-19 infection, the high impreciseness of available information, and not simply recognizing the relevant factors and their effectiveness may cause overestimating and underestimating of factors. This paper puts forward a development of a model with fewer limitations that are more consistent with progressive knowledge about COVID-19. Dealing with the situation of updating the statistical dataset daily, the proposed approach can effectively use the subjectivity inherent in the fuzzy probability interpretation of risk factors using expert knowledge in addition to the statistical dataset. Second, to this uncertainty handling improvement, a specificity-based parameter learning based on the learning network is also added to deal with the complexity aspect of the COVID-19 infection. The learning process helps the proposed structure better adjust the effectiveness of factors. From the achieved results, it is verified that people with advanced age, those with chronic obstructive pulmonary disease, lung cancer, and those having cancer treatments are at higher risk of death if they are infected by COVID-19. Undoubtedly, for vaccination, these three groups should be considered in order to prevent death situations.

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks.

Unpolarized quark and gluon TMD PDFs and FFs at N3LO

In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N3LO) in QCD. The N3LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient functions for TMD FFs exhibit double logarithmic enhancement at small momentum fraction z. We resum such logarithmic terms to the third order in the expansion of αs. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.

Free BMN correlators with more stringy modes

In the type IIB maximally supersymmetric pp-wave background, stringy excited modes are described by BMN (Berenstein-Madalcena-Nastase) operators in the dual $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. In this paper, we continue the studies of higher genus free BMN correlators with more stringy modes, mostly focusing on the case of genus one and four stringy modes in different transverse directions. Surprisingly, we find that the non-negativity of torus two-point functions, which is a consequence of a previously proposed probability interpretation and has been verified in the cases with two and three stringy modes, is no longer true for the case of four or more stringy modes. Nevertheless, the factorization formula, which is also a proposed holographic dictionary relating the torus two-point function to a string diagram calculation, is still valid. We also check the correspondence of planar three-point functions with Green-Schwarz string vertex with many string modes. We discuss some issues in the case of multiple stringy modes in the same transverse direction. Our calculations provide some new perspectives on pp-wave holography.

Renewal Redundant Systems Under the Marshall–Olkin Failure Model. A Probability Analysis

In this paper a two component redundant renewable system operating under the Marshall–Olkin failure model is considered. The purpose of the study is to find analytical expressions for the time dependent and the steady state characteristics of the system. The system cycle process characteristics are analyzed by the use of probability interpretation of the Laplace–Stieltjes transformations (LSTs), and of probability generating functions (PGFs). In this way the long mathematical analytic derivations are avoid. As results of the investigations, the main reliability characteristics of the system—the reliability function and the steady state probabilities—have been found in analytical form. Our approach can be used in the studies of various applications of systems with dependent failures between their elements.

Quantizing time: Interacting clocks and systems

This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the Wheeler-DeWitt equation on a subsystem of the Universe, serving as a clock, being in a state corresponding to a time t. Doing so assigns a conditional state to the rest of the Universe |ψS(t)⟩, referred to as the system. We demonstrate that when the total Hamiltonian appearing in the Wheeler-DeWitt equation contains an interaction term coupling the clock and system, the conditional state |ψS(t)⟩ satisfies a time-nonlocal Schrödinger equation in which the system Hamiltonian is replaced with a self-adjoint integral operator. This time-nonlocal Schrödinger equation is solved perturbatively and three examples of clock-system interactions are examined. One example considered supposes that the clock and system interact via Newtonian gravity, which leads to the system's Hamiltonian developing corrections on the order of G/c4 and inversely proportional to the distance between the clock and system.

CRYPTO-HERMITIAN APPROACH TO THE KLEIN–GORDON EQUATION

We explore the Klein-Gordon equation in the framework of crypto-Hermitian quantum mechanics. Solutions to common problems with probability interpretation and indefinite inner product of the Klein-Gordon equation are proposed.