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Entropy serves as a measure of chaos in systems by representing the average rate of information loss about a phase point's position on the attractor. When dealing with a multifractal system, a single exponent cannot fully describe its dynamics, necessitating a continuous spectrum of exponents, known as the singularity spectrum. From an investor's point of view, a rise in entropy is a signal of abnormal and possibly negative returns. This means he has to expect the unexpected and prepare for it. To explore this, we analyse the New York Stock Exchange (NYSE) U.S. Index as well as its constituents. Through this examination, we assess their multifractal characteristics and identify market conditions (bearish/bullish markets) using entropy, an effective method for recognizing fluctuating fractal markets. Our findings challenge conventional beliefs by demonstrating that price declines lead to increased entropy, contrary to some studies in the literature that suggest that reduced entropy in market crises implies more determinism. Instead, we propose that bear markets are likely to exhibit higher entropy, indicating a greater chance of unexpected extreme events. Moreover, our study reveals a power-law behaviour and indicates the absence of variance. [ABSTRACT FROM AUTHOR]

The objective of this study is to evaluate assets' performance by considering the exit time within the risk measurement framework alongside Shannon entropy and, alternatively, excluding these factors, which can be used to create a portfolio aligned with short- or long-term objectives. This portfolio effectively balances the potential risks and returns, guiding investors to make decisions that are in line with their financial goals. To assess the performance, we used data envelopment analysis (DEA), whereby we utilized the risk measure as an input and the mean return as an output. The stop point probability–CVaR (SPP-CVaR) was the risk measurement used when considering the exit time. We calculated the SPP-CVaR by converting the risk-neutral density to the real-world density, calibrating the parameters, running simulations for price paths, setting the stop-profit points, determining the exit times, and calculating the SPP-CVaR for each stop-profit point. To account for negative data and to incorporate the exit time, we have proposed a model that integrates the mean return and SPP-CVaR, utilizing DEA. The resulting inefficiency scores of this model were compared with those of the mean-CVaR model, which calculates the risk across the entire time horizon and does not take the exit time and Shannon entropy into account. To accomplish this, an analysis was conducted on a portfolio that included a variety of stocks, cryptocurrencies, commodities, and precious metals. The empirical application demonstrated the enhancement of asset selection for both short-term and long-term investments through the combined use of Shannon entropy and the exit time. [ABSTRACT FROM AUTHOR]

Failure mode and effects analysis (FMEA) is a proactive risk management approach. Risk management under uncertainty with the FMEA method has attracted a lot of attention. The Dempster–Shafer (D-S) evidence theory is a popular approximate reasoning theory for addressing uncertain information and it can be adopted in FMEA for uncertain information processing because of its flexibility and superiority in coping with uncertain and subjective assessments. The assessments coming from FMEA experts may include highly conflicting evidence for information fusion in the framework of D-S evidence theory. Therefore, in this paper, we propose an improved FMEA method based on the Gaussian model and D-S evidence theory to handle the subjective assessments of FMEA experts and apply it to deal with FMEA in the air system of an aero turbofan engine. First, we define three kinds of generalized scaling by Gaussian distribution characteristics to deal with potential highly conflicting evidence in the assessments. Then, we fuse expert assessments with the Dempster combination rule. Finally, we obtain the risk priority number to rank the risk level of the FMEA items. The experimental results show that the method is effective and reasonable in dealing with risk analysis in the air system of an aero turbofan engine. [ABSTRACT FROM AUTHOR]

The Kelly criterion determines optimal bet sizes that maximize long-term growth. While growth is definitely an important consideration, the focus on growth alone can lead to significant drawdowns, leading to psychological discomfort for a risk-taker. Path-dependent risk measures, such as drawdown risk, provide a means to assess the risk of significant portfolio retracements. In this paper, we provide a flexible framework for assessing path dependent risk for a trading or investment operation. Given a certain set of profitable trading characteristics, a risk-taker who maximizes expected growth can still be faced with significant drawdowns to the point where a strategy becomes unsustainable. We demonstrate, through a series of experiments, the importance of path dependent risks in the case of outcomes subject to various return distributions. Based on Monte Carlo simulation, we analyze the medium-term behavior of different cumulative return paths and study the impact of different return outcome distributions. We show that in the case of heavier tailed outcomes, extra care is needed, and optimal might not be so optimal in the end. [ABSTRACT FROM AUTHOR]

This paper provides a comparative analysis of stock market dynamics of the 1987 and 2008 financial crises and discusses the extent to which risk management measures based on entropy can be successful in predicting aggregate market expectations. We find that the Tsallis entropy is more appropriate for the short and sudden market crash of 1987, while the approximate entropy is the dominant predictor of the prolonged, fundamental crisis of 2008. We conclude by suggesting the use of entropy as a market sentiment indicator in technical analysis. [ABSTRACT FROM AUTHOR]

Portfolio selection in the financial literature has essentially been analyzed under two central assumptions: full knowledge of the joint probability distribution of the returns of the securities that will comprise the target portfolio; and investors' preferences are expressed through a utility function. In the real world, operators build portfolios under risk constraints which are expressed both by their clients and regulators and which bear on the maximal loss that may be generated over a given time period at a given confidence level (the so-called Value at Risk of the position). Interestingly, in the finance literature, a serious discussion of how much or little is known from a probabilistic standpoint about the multi-dimensional density of the assets' returns seems to be of limited relevance. Our approach in contrast is to highlight these issues and then adopt throughout a framework of entropy maximization to represent the real world ignorance of the "true" probability distributions, both univariate and multivariate, of traded securities' returns. In this setting, we identify the optimal portfolio under a number of downside risk constraints. Two interesting results are exhibited: (i) the left- tail constraints are sufficiently powerful to override all other considerations in the conventional theory; (ii) the "barbell portfolio" (maximal certainty/ low risk in one set of holdings, maximal uncertainty in another), which is quite familiar to traders, naturally emerges in our construction. [ABSTRACT FROM AUTHOR]

As a typical tool of risk analysis in practical engineering, failure mode and effects analysis (FMEA) theory is a well known method for risk prediction and prevention. However, how to quantify the uncertainty of the subjective assessments from FMEA experts and aggregate the corresponding uncertainty to the classical FMEA approach still needs further study. In this paper, we argue that the subjective assessments of FMEA experts can be adopted to model the weight of each FMEA expert, which can be regarded as a data-driven method for ambiguity information modeling in FMEA method. Based on this new perspective, a modified FMEA approach is proposed, where the subjective uncertainty of FMEA experts is handled in the framework of Dempster–Shafer evidence theory (DST). In the improved FMEA approach, the ambiguity measure (AM) which is an entropy-like uncertainty measure in DST framework is applied to quantify the uncertainty degree of each FMEA expert. Then, the classical risk priority number (RPN) model is improved by aggregating an AM-based weight factor into the RPN function. A case study based on the new RPN model in aircraft turbine rotor blades verifies the applicable and useful of the proposed FMEA approach. [ABSTRACT FROM AUTHOR]