We discuss a class of risk measures for portfolio optimization with linear loss functions, where the random returns of financial instruments have a multivariate elliptical distribution. Under this setting we pay special attention to two risk measures, Value-at-Risk and Conditional-Value-at-Risk...

Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model,...

Coping with the uncertainties of future outcomes is a fundamental theme in finance in a stochastic environment. In the field of stochastic programming, which grown from the traditions of linear and quadratic programming, constrains on future outcomes have commonly been relaxed to the penalty...

In this paper we derive closed-form solutions for the cumulative density function and the average value-at-risk for five subclasses of the infinitely divisible distributions: classical tempered stable distribution, Kim-Rachev distribution, modified tempered stable distribution, normal tempered...

Risk analysis and management currently have a strong presence in financial institutions, where high performance and energy efficiency are key requirements for acceleration systems, especially when it comes to intraday analysis. In this regard, we approach the estimation of the widely-employed...

We discuss a class of risk measures for portfolio optimization with linear loss functions, where the random returns of financial instruments have a multivariate elliptical distribution. Under this setting we pay special attention to two risk measures, Value-at-Risk and Conditional-Value-at-Risk...

Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model,...

Cryptocurrency investments are often perceived as uncertain and risky. In this study, we assessed if this is indeed the case, using a sample of seven cryptocurrencies and considered a period that encompassed the first real global shock in the life of these relatively new financial assets, the...

General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such measures include standard deviation as a special case but need not be symmetric with respect to ups and downs. Their...

Nobel Laureate Harry Markowitz is often referred to as the 'founder of Modern portfolio theory' and deservedly so given his enormous influence on the money management industry.1 However, it is my contention that he should also be referred to as the 'founder of Modern Risk Management' since his...