International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Nobel-Prize-winning Black-Scholes equations are actively used to estimate the price of options and other financial instruments. In practice, they provide a good estimate for the price, but the problem is that their original derivation is based on many simplifying statistical assumptions which are, in general, not valid for financial time series. The fact that these equations are effective way beyond their usual assumptions leads to a natural conclusion that there must be an alternative derivation for these equations, a derivation that does not use the usual too-strong assumptions. In this paper, we provide such a derivation in which the only substantial assumption is a natural symmetry: namely, scale-invariance of the corresponding processes. Scale-invariance also allows us to describe possible generalizations of Black-Scholes equations, generalizations that we hope will lead to even more accurate estimates for the corresponding prices.

A new product can be produced and sold in a market thanks to the entrance of a patent holder into the market. This market is divided into submarkets controlled by only some firms and the profit attainable in each submarket is uncertain. In this paper, this situation is studied by means of cooperative games under interval uncertainty. We consider different ways of allocating the interval profit among the firms. One of these is the interval $\mathcal{T}$-value, which is defined for interval games satisfying some conditions. Efficient interval solutions in terms of the market data are provided.

In the past, in many areas, the best prediction models were linear and nonlinear parametric models. In the last decade, in many application areas, deep learning has shown to lead to more accurate predictions than the parametric models. Deep learning-based predictions are reasonably accurate, but not perfect. How can we achieve better accuracy? To achieve this objective, we propose to combine neural networks with parametric model: namely, to train neural networks not on the original data, but on the differences between the actual data and the predictions of the parametric model. On the example of predicting currency exchange rate, we show that this idea indeed leads to more accurate predictions.

In many practical situations, it is desirable to predict binary (“yes”–“no”) decisions made by people. The traditional approach to this prediction assumes that the utility linearly depends on the corresponding parameters, and that the distribution of the difference between predicted and actual utility is symmetric — usually normal or logistic; the corresponding techniques are known as, correspondingly, probit and logit. In real life, utility often non-linearly depends on the parameters, and the corresponding distributions are asymmetric (skewed). There are techniques for dealing with non-linearity; the most widely used such technique — called kink regression — uses piece-wise linear approximations to the utility. There are also techniques that take into account the distribution’s asymmetry; usually, they are based on using special asymmetric distributions: skew-normal and skew-logistic. In this paper, we show how these two techniques to be combined to take into account both non-linearity and asymmetry. On a real-life example, we show that the new technique indeed leads to a better description of human binary decision-making.

When considering the medical care costs data with a high proportion of zero items of two inpatient groups, comparing them can be estimated using confidence intervals for the ratio of the means of two delta-lognormal distributions. The Bayesian credible interval-based uniform-beta prior (BCI_h-UB) is proposed and compared with the generalized confidence interval (GCI), fiducial GCI (FGCI), the method of variance estimates recovery (MOVER), BCI_h based on Jeffreys’ rule prior (BCI_h-JR), and BCI_h based on the normal-gamma prior (BCI_h-NG). The coverage probability (CP), average length (AL), and lower and upper error rates were the performance measures applied for assessing the methods through a Monte Carlo simulation. A numerical evaluation showed that BCI_h-UB had much better CP and AL than the others even with a large difference between the variances and with a high proportion of zero. Finally, to illustrate the efficacy of BCI_h-UB, the methods were applied to two sets of medical care costs data.

In this paper we investigate an insurance continuous-time risk model when the claim sizes and inter-arrival times are m-dependent random variables. We provide an upper exponential bound for the ruin probability.

One of the main objectives of econometrics is to predict future values of important economics-related quantities, such as unemployment level, stock prices, currency exchange rates, etc. — and especially to predict how different possible economy-boosting measures will affect these quantities. To perform this prediction, we design a model of such effect and train it on the available data. Usually, the daily (or weekly) data are used for this training. However, economics-related quantities fluctuate all the time. So, for each moment of time (e.g., for each day) instead of a single value of the corresponding quantity, we have smallest and largest daily values — i.e., the interval range of daily values. At first glance, it may seem that using both endpoints of this interval for training will lead to more accurate predictions, but in reality, predictions become less accurate. Predictions become more accurate if we only use midpoints of the corresponding intervals. Several recent papers showed that even more accurate predictions are possible if we allow general convex combinations of the intervals’ endpoints — and select the corresponding coefficients so as to best fit the data. In this paper, we provide a theoretical explanation for these results.

In this paper, we emphasize and elaborate on two important and relatively new aspects in uncertainty analysis in order to increase the credibility of empirical results in statistics in general, and in econometrics in particular, namely, the problem of partial identification, and the use of random set statistics. We elaborate on the current interests in partially identified models, exemplified by econometric structures involving copulas. We spell out the rationale and the statistical methods based upon random set theory for analyzing partial identification problem towards credible econometrics.

The Black-Litterman asset allocation model is an extended portfolio management model to construct optimal portfolios by combining the market equilibrium with investor views into asset allocation decisions. In this paper we apply Black-Litterman model for portfolio optimization on Vietnames stock market. We chose ARIMA methodology utilized in financial econonometrics to predict the views of investor which are used as inputs of the Black-Litterman asset allocation process to find optimal portfolio and weights.

In many practical applications, the dynamics of different quantities is reasonably well described by linear equations. In economics, such linear dynamical models are known as vector autoregressive (VAR) models. These linear models are, however, only approximate. The deviations of the actual value of each quantity from the predictions of the linear model are usually well described by normal or Student-t distributions. To complete the description of the joint distribution of all these deviations, we need to supplement these marginal distributions with the information about the corresponding copula. To describe this dependence, in the past, researchers followed the usual idea of trying copulas from several standard families: Gaussian, Student, Clayton, Frank, Gumbel, and Joe families. To get a better description, we propose to also use convex combinations of copulas from different families; such convex combinations are known as mixed copulas. On the example of the dynamics of US macroeconomic data, including GDP, unemployment, consumer price index, and the real effective exchange rate, we show that mixed copulas indeed lead to a better description of the actual data. Specifically, it turns out that the best description is obtained if we use a convex combination of Student and Frank copulas.