New risk measures for variance distortion and catastrophic financial risk measures

In recent years, expectation distortion risk measures have been widely used in financial and insurance applications due to their attractive properties. The author introduced two new classes of financial risk measures “VaR raised to the power of t” and “ES raised to the power of t” in his works and also investigated the issue of the belonging of these risk measures to the class of risk measures of expectation distortion, and described the corresponding distortion functions. The aim of this study is to introduce a new concept of variance distortion risk measures, which opens up a significant area for investigating the properties of these risk measures that may be useful in applications. The paper proposes a method of finding new variance distortion risk measures that can be used to acquire risk measures with special properties. As a result of the study, it was found that the class of risk measures of variance distortion includes risk measures that are in a certain way related to “VaR raised to the power of t” and “ES raised to the power of t” measures. The article describes the composite method for constructing new variance distortion functions and corresponding distortion risk measures. This method is used to build a large set of examples of variance distortion risk measures that can be used in assessing certain financial risks of a catastrophic nature. The author concludes that the study of the variance distortion risk measures introduced in this paper can be used both for the development of theoretical risk management methods and in the practice of business risk management in assessing unlikely risks of high catastrophe.

Prediction of record values by using quantile regression curves and distortion functions

The purpose of the paper is to provide a general method based on conditional quantile curves to predict record values from preceding records. The predictions are based on conditional median (or median regression) curves. Moreover, conditional quantiles curves are used to provide confidence bands for these predictions. The method is based on the recently introduced concept of multivariate distorted distributions that are used instead of copulas to represent the dependence structure. This concept allows us to compute the conditional quantile curves in a simple way. The theoretical findings are illustrated with a non-parametric model (standard uniform), two parametric models (exponential and Pareto), and a non-parametric procedure for the general case. A real data set and a simulated case study in reliability are analysed.

An interactive system for muscle and fat tissue identification of the lumbar spine using semantic segmentation

We introduce a system that allows the immediate identification and inspection of fat and muscle structures around the lumbar spine as a means of orthopaedic diagnostics before surgical treatment. The system comprises a backend component that accepts MRI data from a web-based interactive frontend as REST requests. The MRI data is passed through a U-net model, fine-tuned on lumbar MRI images, to generate segmentation masks of fat and muscle areas. The result is sent back to the frontend that functions as an inspection tool. For the model training, 4000 MRI images from 108 patients were used in a k-fold cross-validation study with k = 10. The model training was performed over 25-30 epochs. We applied shift, scale, and rotation operations as well as elastic deformation and distortion functions for image augmentation and a combined objective function using Dice and Focal loss. The trained models reached a mean dice score of 0.83 and 0.52 and a mean area error tissue of 0.1 and 0.3 for muscle and fat tissue, respectively. The interactive webbased frontend as an inspection tool was evaluated by clinicians to be suitable for the exploration of patient data as well as the assessment of segmentation results. We developed a system that uses semantic segmentation to identify fat and muscle tissue areas in MRI images of the lumbar spine. Further improvements should focus on the segmentation accuracy of fat tissue, as it is a determining factor in surgical decisionmaking. To our knowledge, this is the first system that automatically provides semantic information of the respective lumbar tissues.

Using the Semantic Information G Measure to Explain and Extend Rate-Distortion Functions and Maximum Entropy Distributions

In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual Information (MMI) distributions and ME distributions are expressed by Bayes-like formulas, including Negative Exponential Functions (NEFs) and partition functions. Why do these non-probability functions exist in Bayes-like formulas? On the other hand, the rate-distortion function has three disadvantages: (1) the distortion function is subjectively defined; (2) the definition of the distortion function between instances and labels is often difficult; (3) it cannot be used for data compression according to the labels’ semantic meanings. The author has proposed using the semantic information G measure with both statistical probability and logical probability before. We can now explain NEFs as truth functions, partition functions as logical probabilities, Bayes-like formulas as semantic Bayes’ formulas, MMI as Semantic Mutual Information (SMI), and ME as extreme ME minus SMI. In overcoming the above disadvantages, this paper sets up the relationship between truth functions and distortion functions, obtains truth functions from samples by machine learning, and constructs constraint conditions with truth functions to extend rate-distortion functions. Two examples are used to help readers understand the MMI iteration and to support the theoretical results. Using truth functions and the semantic information G measure, we can combine machine learning and data compression, including semantic compression. We need further studies to explore general data compression and recovery, according to the semantic meaning.

Improving the Predictive Value of Phytochrome Photoequilibrium: Consideration of Spectral Distortion Within a Leaf

The ratio of active phytochrome (Pfr) to total phytochrome (Pr + Pfr), called phytochrome photo-equilibrium (PPE; also called phytochrome photostationary state, PSS) has been used to explain shade avoidance responses in both natural and controlled environments. PPE is commonly estimated using measurements of the spectral photon distribution (SPD) above the canopy and photoconversion coefficients. This approach has effectively predicted morphological responses when only red and far-red (FR) photon fluxes have varied, but controlled environment research often utilizes unique ratios of wavelengths so a more rigorous evaluation of the predictive ability of PPE on morphology is warranted. Estimations of PPE have rarely incorporated the optical effects of spectral distortion within a leaf caused by pigment absorbance and photon scattering. We studied stem elongation rate in the model plant cucumber under diverse spectral backgrounds over a range of one to 45% FR (total photon flux density, 400–750 nm, of 400 μmol m–2 s–1) and found that PPE was not predictive when blue and green varied. Preferential absorption of red and blue photons by chlorophyll results in an SPD that is relatively enriched in green and FR at the phytochrome molecule within a cell. This can be described by spectral distortion functions for specific layers of a leaf. Multiplying the photoconversion coefficients by these distortion functions yields photoconversion weighting factors that predict phytochrome conversion at the site of photon perception within leaf tissue. Incorporating spectral distortion improved the predictive value of PPE when phytochrome was assumed to be homogeneously distributed within the whole leaf. In a supporting study, the herbicide norflurazon was used to remove chlorophyll in seedlings. Using distortion functions unique to either green or white cotyledons, we came to the same conclusions as with whole plants in the longer-term study. Leaves of most species have similar spectral absorbance so this approach for predicting PPE should be broadly applicable. We provide a table of the photoconversion weighting factors. Our analysis indicates that the simple, intuitive ratio of FR (700–750 nm) to total photon flux (far-red fraction) is also a reliable predictor of morphological responses like stem length.

Computing Sensitivities for Distortion Risk Measures

Distortion risk measure, defined by an integral of a distorted tail probability, has been widely used in behavioral economics and risk management as an alternative to expected utility. The sensitivity of the distortion risk measure is a functional of certain distribution sensitivities. We propose a new sensitivity estimator for the distortion risk measure that uses generalized likelihood ratio estimators for distribution sensitivities as input and establish a central limit theorem for the new estimator. The proposed estimator can handle discontinuous sample paths and distortion functions.

BEHAVIORAL PORTFOLIO CHOICE UNDER HYPERBOLIC ABSOLUTE RISK AVERSION

This paper studies the optimal investment problem for a behavioral investor with probability distortion functions and an S-shaped utility function whose utility on gains satisfies the Inada condition at infinity, albeit not necessarily at zero, in a complete continuous-time financial market model. In particular, a piecewise utility function with hyperbolic absolute risk aversion (HARA) is applied. The considered behavioral framework, cumulative prospect theory (CPT), was originally introduced by [A. Tversky & D. Kahneman (1992) Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty 5 (4), 297–323]. The utility model allows for increasing, constant or decreasing relative risk aversion. The continuous-time portfolio selection problem under the S-shaped HARA utility function in combination with probability distortion functions on gains and losses is solved theoretically for the first time, the optimal terminal wealth and its replicating wealth process and investment strategy are stated. In addition, conditions on the utility and the probability distortion functions for well-posedness and closed-form solutions are provided. A specific probability distortion function family is presented which fulfills all those requirements. This generalizes the work by [H. Jin & X. Y. Zhou (2008) Behavioral portfolio selection in continuous time, Mathematical Finance 18 (3), 385–426]. Finally, a numerical case study is carried out to illustrate the impact of the utility function and the probability distortion functions.