scholarly journals Risk Measurement by G-Expected Shortfall

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Ziting Pei ◽  
Xuhui Wang ◽  
Xingye Yue
Keyword(s):  
Explicit Formula ◽  
Empirical Analysis ◽  
Risk Measure ◽  
Computational Cost ◽  
Expected Shortfall ◽  
Risk Measurement ◽  
Worst Case ◽  
New Type ◽  
The Empirical Analysis ◽  
Low Computational Cost

G-expected shortfall (G-ES), which is a new type of worst-case expected shortfall (ES), is defined as measuring risk under infinite distributions induced by volatility uncertainty. Compared with extant notions of the worst-case ES, the G-ES can be computed using an explicit formula with low computational cost. We also conduct backtests for the G-ES. The empirical analysis demonstrates that the G-ES is a reliable risk measure.

scholarly journals Time Complexity Analysis of the Binary Tree Roll Algorithm

2017 ◽  
Vol 12 (2) ◽  
Author(s):  
Adrijan Božinovski ◽  
George Tanev ◽  
Biljana Stojčevska ◽  
Veno Pačovski ◽  
Nevena Ackovska
Keyword(s):  
Theoretical Analysis ◽  
Empirical Analysis ◽  
Binary Tree ◽  
Time Complexity ◽  
Recurrence Relations ◽  
Complexity Analysis ◽  
Worst Case ◽  
Average Case ◽  
The Empirical Analysis

This paper presents the time complexity analysis of the Binary Tree Roll algorithm. The time complexity is analyzed theoretically and the results are then confirmed empirically. The theoretical analysis consists of finding recurrence relations for the time complexity, and solving them using various methods. The empirical analysis consists of exhaustively testing all trees with given numbers of nodes  and counting the minimum and maximum steps necessary to complete the roll algorithm. The time complexity is shown, both theoretically and empirically, to be linear in the best case and quadratic in the worst case, whereas its average case is shown to be dominantly linear for trees with a relatively small number of nodes and dominantly quadratic otherwise.

scholarly journals Space Complexity Analysis of the Binary Tree Roll Algorithm

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Adrijan Božinovski ◽  
George Tanev ◽  
Biljana Stojčevska ◽  
Veno Pačovski ◽  
Nevena Ackovska
Keyword(s):  
Theoretical Analysis ◽  
Empirical Analysis ◽  
Binary Tree ◽  
Complexity Analysis ◽  
Space Complexity ◽  
Worst Case ◽  
Average Case ◽  
Tree Topologies ◽  
The Given ◽  
The Empirical Analysis

This paper presents the space complexity analysis of the Binary Tree Roll algorithm. The space complexity is analyzed theoretically and the results are then confirmed empirically. The theoretical analysis consists of determining the amount of memory occupied during the execution of the algorithm and deriving functions of it, in terms of the number of nodes of the tree n, for the worst - and best-case scenarios. The empirical analysis of the space complexity consists of measuring the maximum and minimum amounts of memory occupied during the execution of the algorithm, for all binary tree topologies with the given number of nodes. The space complexity is shown, both theoretically and empirically, to be logarithmic in the best case and linear in the worst case, whereas its average case is shown to be dominantly logarithmic.

scholarly journals A New Generalized Projection and Its Application to Acceleration of Audio Declipping

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 105
Author(s):  
Pavel Rajmic ◽  
Pavel Záviška ◽  
Vítězslav Veselý ◽  
Ondřej Mokrý
Keyword(s):  
Signal Processing ◽  
Convex Optimization ◽  
Linear Operator ◽  
Explicit Formula ◽  
Convex Sets ◽  
State Of The Art ◽  
Computational Cost ◽  
The Other ◽  
Speed Up ◽  
Low Computational Cost

In convex optimization, it is often inevitable to work with projectors onto convex sets composed with a linear operator. Such a need arises from both the theory and applications, with signal processing being a prominent and broad field where convex optimization has been used recently. In this article, a novel projector is presented, which generalizes previous results in that it admits to work with a broader family of linear transforms when compared with the state of the art but, on the other hand, it is limited to box-type convex sets in the transformed domain. The new projector is described by an explicit formula, which makes it simple to implement and requires a low computational cost. The projector is interpreted within the framework of the so-called proximal splitting theory. The convenience of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

scholarly journals Expected Shortfall Reliability—Added Value of Traditional Statistics and Advanced Artificial Intelligence for Market Risk Measurement Purposes

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2142
Author(s):  
Santiago Carrillo Carrillo Menéndez ◽  
Bertrand Kian Hassani
Keyword(s):  
Risk Measure ◽  
Sampling Technique ◽  
Market Risk ◽  
Expected Shortfall ◽  
Risk Measurement ◽  
Added Value ◽  
Sufficient Information ◽  
Distribution Fitting ◽  
Expectation Maximisation ◽  
Capital Standard

The Fundamental Review of the Trading Book is a market risk measurement and management regulation recently issued by the Basel Committee. This reform, often referred to as “Basel IV”, intends to strengthen the financial system. The newest capital standard relies on the use of the Expected Shortfall. This risk measure requires to get sufficient information in the tails to ensure its reliability, as this one has to be alimented by a sufficient quantity of relevant data (above the 97.5 percentile in the case of the regulation or interest). In this paper, after discussing the relevant features of Expected Shortfall for risk measurement purposes, we present and compare several methods allowing to ensure the reliability of the risk measure by generating information in the tails. We discuss these approaches with respect to their relevance considering the underlying situation when it comes to available data, allowing practitioners to select the most appropriate approach. We apply traditional statistical methodologies, for instance distribution fitting, kernel density estimation, Gaussian mixtures and conditional fitting by Expectation-Maximisation as well as AI related strategies, for instance a Synthetic Minority Over-sampling Technique implemented in a regression environment and Generative Adversarial Nets.

The Word Class Adjective in English Business Magazines Online

2018 ◽  
Vol 6 (2) ◽  
pp. 99-115
Author(s):  
Borislav Marušić ◽  
Sanda Katavić-Čaušić
Keyword(s):  
Empirical Study ◽  
Empirical Analysis ◽  
Word Formation ◽  
Word Class ◽  
Business English ◽  
Starting Point ◽  
Comprehensive Picture ◽  
English Syntax ◽  
The Empirical Analysis ◽  
Insight Into

Abstract The aim of this paper is to research the word class adjective in one sequence of the ESP: Business English, more precisely English business magazines online. It is an empirical study on the corpus taken from a variety of business magazines online. The empirical analysis allows a comprehensive insight into the word class adjective in this variety of Business English and makes its contribution to English syntax, semantics and word formation. The syntactic part analyses the adjective position in the sentence. The semantic part of the study identifies the most common adjectives that appear in English business magazines online. Most of the analysis is devoted to the word formation of the adjectives found in the corpus. The corpus is analysed in such a way that it enables its division into compounds, derivatives and conversions. The results obtained in this way will give a comprehensive picture of the word class adjective in this type of Business English and can act as a starting point for further research of the word class adjective.

ICT SMEs, Performance, Absorptive Capacity and Transformative Capacity

2019 ◽  
Vol 118 (3) ◽  
pp. 178-188
Author(s):  
Yeon-Sung Cho ◽  
Kyung-Il Khoe
Keyword(s):  
Firm Performance ◽  
Market Orientation ◽  
Empirical Analysis ◽  
Absorptive Capacity ◽  
Latent Variables ◽  
Equation Modeling ◽  
Transformative Capacity ◽  
The Impact ◽  
The Empirical Analysis ◽  
Innovative Capacity

This study intends to integrate the relationship of market orientation, innovative capacity and firm performance to Information and Communication Technology(ICT) SMEs. The purpose of this study is to identify the role of absorptive capacity and transformative capacity that affect the performance of ICT SMEs. Hypotheses were established between five latent variables. A total of six hypotheses were established including the moderated effects of absorptive capacity and transformative capacity. Of the data collected after the survey, 112 valid surveys were selected as the final sample, except for 17 questionnaires with high non - response and insincere response. The empirical analysis of this study used smartpls3.0, Partial Least Squares (PLS), a variance-based structural equation modeling. The empirical analysis of this study revealed that the impact of market orientation on innovative capacity was significant. Moreover, the innovative capacity had a positive effect on the performance of ICT SMEs. In addition, the absorptive activity had a positive moderated effect between the market orientation and the innovative capacity. On the other hand, the transformative capacity showed a positive moderated effect in relation to innovative capacity and firm performance. Our empirical results have demonstrated the importance of knowledge based capacity in the ICT SMEs.

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