CHEBYSHEV INEQUALITIES WITH LAW-INVARIANT DEVIATION MEASURES

2009 ◽  
Vol 24 (1) ◽  
pp. 145-170 ◽  
Author(s):  
Bogdan Grechuk ◽  
Anton Molyboha ◽  
Michael Zabarankin
Keyword(s):  
At Risk ◽  
Exchange Rate ◽  
Value At Risk ◽  
Random Variables ◽  
Conditional Value At Risk ◽  
Mean Absolute Deviation ◽  
Absolute Deviation ◽  
Kolmogorov Inequality ◽  
The Exchange Rate ◽  
Chebyshev Inequalities

The consistency of law-invariant general deviation measures with concave ordering has been used to generalize the 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 ordering. This approach has been applied for constructing the Chebyshev and Kolmogorov inequalities with law-invariant deviation measures—in particular with mean absolute deviation, lower semideviation and conditional value-at-risk deviation. Additionally, an advantage of the Kolmogorov inequality with certain deviation measures has been illustrated in estimating the probability of the exchange rate of two currencies to be within specified bounds.

scholarly journals Value at risk using smoothing techniques: a proposal in the foreign exchange market

2018 ◽  
Vol 16 (2) ◽  
pp. 99-110
Author(s):  
Jorge Luis Reyes García ◽  
Arturo Morales Castro
Keyword(s):  
At Risk ◽  
Monte Carlo ◽  
Exchange Rate ◽  
Value At Risk ◽  
Foreign Exchange Market ◽  
Financial Assets ◽  
Exchange Market ◽  
Historical Simulation ◽  
Simulation Monte Carlo ◽  
The Exchange Rate

One of the main problems that are exposed companies and financial institutions in Mexico is the volatility in the exchange rate Peso/Dollar when operating or in the valuation of financial assets. This article analyzes and compares the behavior of value at risk [VAR] under three different methodologies: historical simulation, Monte Carlo Simulation and straightening. An application to the exchange rate in periods of Precrisis, Postcrisis and economic crisis of 2008 is performed to look at the implications of the VAR calculation. We conclude that the straightening VAR methodology is more accurate.ResumenUno de los principales problemas a los que se encuentran expuestas las empresas e instituciones financieras en México es la volatilidad en el tipo de cambio Peso/Dólar al realizar operaciones o en la valuación de activos financieros. En el presente artículo se analiza y se compara el comportamiento del Valor en Riesgo [VAR] bajo tres metodologías diferentes: Simulación Histórica, Simulación Montecarlo y Alisado. Se realiza una aplicación al tipo de cambio en los periodos de Precrisis, Crisis y Postcrisis económica de 2008 para observar las implicaciones del cálculo del Valor en Riesgo. Se concluye que la metodología del VAR alisado es más precisa.ResumoUm dos principais problemas que são expostos empresas e instituições financeiras no México é a volatilidade na taxa de câmbio Peso / dólar para executar operações ou valorização dos activos financeiros. Neste artigo vamos analisar o valor comportamento e comparados at risk [ VaR ] em três diferentes metodologias : Simulação histórica , Simulação de Monte Carlo e alisamento. é realizada uma aplicação à taxa durante os períodos de crise Pre, Crise crise económica e Pós 2008 para observar as implicações de Value at Risk cálculo . Concluiu- se que a metodologia VaR alisamento é mais preciso.

A Fourier approach to the computation of conditional value-at-risk and optimized certainty equivalents

2014 ◽  
Vol 16 (6) ◽  
pp. 3-29 ◽  
Author(s):  
Samuel Drapeau ◽  
Michael Kupper ◽  
Antonis Papapantoleon
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Conditional Value At Risk ◽  
Certainty Equivalents
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