Special Issue "Advances in Multivariate Analysis and Their Applications in Actuarial and Financial Economics"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: closed (31 March 2021).

Special Issue Editors

Prof. Dr. José María Sarabia
E-Mail Website
Guest Editor
Department of Quantitative Methods, CUNEF University, Leonardo Prieto Castro 2, 28040 Madrid, Spain
Interests: distribution theory; economic inequality; risk analysis; informetrics; multivariate analysis
Prof. Dr. Montserrat Guillén
E-Mail Website
Guest Editor
Department of Econometrics, Riskcenter-IREA Universitat de Barcelona Av. Diagonal, 690 08034 Barcelona, Spain
Interests: risk; insurance; actuarial statistics; long-term care insurance; experience rating; statistical methods for insurance and finance, automobile fraud detection, quantitative methods for risk management; longevity; pension-saving investment; risk analytics
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

The modern multivariate analysis includes all topics and techniques in classical multivariate analysis for modeling different structures and types of data, including factor analysis, cluster analysis, discriminant analysis, regression and multivariate time series, and multivariate discrete and continuous distributions and inferential topics. Other, more recent aspects are functional and high-dimensional data analysis, modeling using copulas, multivariate extreme-value theory, spatial statistics, as well as new challenges in big data and machine learning.

This Special Issue focuses on the applications of all these techniques in insurance and finance. Some applications in insurance include generalized linear models and generalized additive models, specification of multivariate risk distributions, fraud detection, insurance pricing in multivariate settings, individual and collective risk models under dependence, aggregation and capital allocation, multivariate risk and distorted measures, measures in risk assessment, multivariate credibility formulas, big data and machine learning algorithms, etc.

Applications of multivariate analysis in finance include multivariate time series analysis for financial data, financial econometrics, credit scoring techniques, new classes of flexible copulas for modeling financial variables, portfolio selection, multivariate financial risk measures, modeling dependent stock prices and option pricing, market dynamics and prediction, operational risks, etc.

Relevant empirical applications with a financial and/or an insurance content are welcome.

Prof. Dr. José María Sarabia
Prof. Montserrat Guillén
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Multivariate distributions
  • Copulas
  • Risk measurement
  • Portfolio selection
  • Heavy tails
  • Causal and predictive modeling

Published Papers (11 papers)

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Research

Article
Debt-by-Price Ratio, End-of-Year Economic Growth, and Long-Term Prediction of Stock Returns
Mathematics 2021, 9(13), 1550; https://doi.org/10.3390/math9131550 - 01 Jul 2021
Viewed by 396
Abstract
With the prominent role of government debt in economic growth in recent decades, one would expect that government debt alongside economic growth to be a risk factor priced in the time series of stock returns. In this paper, this idea is investigated by [...] Read more.
With the prominent role of government debt in economic growth in recent decades, one would expect that government debt alongside economic growth to be a risk factor priced in the time series of stock returns. In this paper, this idea is investigated by applying a nonparametric model, namely, a local-linear kernel smoother with the aim of forecasting long-term stock returns where the model and smoothing parameters are chosen by cross-validation. While a wide range of predictive variables are examined, we find that our newly introduced debt-by-price ratio and the third to fourth quarter economic growth are robust predictors of stock returns, beating the well-known predictive variables in the literature by a significant difference. The combination of these two covariates can explain almost 30% variation of stock returns at a one-year horizon. This is very crucial considering the difficulty in capturing even a small proportion of movements in stock returns. Full article
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Article
A New Kernel Estimator of Copulas Based on Beta Quantile Transformations
Mathematics 2021, 9(10), 1078; https://doi.org/10.3390/math9101078 - 11 May 2021
Viewed by 340
Abstract
A copula is a multivariate cumulative distribution function with marginal distributions Uniform(0,1). For this reason, a classical kernel estimator does not work and this estimator needs to be corrected at boundaries, [...] Read more.
A copula is a multivariate cumulative distribution function with marginal distributions Uniform(0,1). For this reason, a classical kernel estimator does not work and this estimator needs to be corrected at boundaries, which increases the difficulty of the estimation and, in practice, the bias boundary correction might not provide the desired improvement. A quantile transformation of marginals is a way to improve the classical kernel approach. This paper shows a Beta quantile transformation to be optimal and analyses a kernel estimator based on this transformation. Furthermore, the basic properties that allow the new estimator to be used for inference on extreme value copulas are tested. The results of a simulation study show how the new nonparametric estimator improves alternative kernel estimators of copulas. We illustrate our proposal with a financial risk data analysis. Full article
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Article
How to Explain the Cross-Section of Equity Returns through Common Principal Components
Mathematics 2021, 9(9), 1011; https://doi.org/10.3390/math9091011 - 29 Apr 2021
Viewed by 470
Abstract
In this paper, we propose a procedure to obtain and test multifactor models based on statistical and financial factors. A major issue in the factor literature is to select the factors included in the model, as well as the construction of the portfolios. [...] Read more.
In this paper, we propose a procedure to obtain and test multifactor models based on statistical and financial factors. A major issue in the factor literature is to select the factors included in the model, as well as the construction of the portfolios. We deal with this matter using a dimensionality reduction technique designed to work with several groups of data called Common Principal Components. A block-bootstrap methodology is developed to assess the validity of the model and the significance of the parameters involved. Data come from Reuters, correspond to nearly 1250 EU companies, and span from October 2009 to October 2019. We also compare our bootstrap-based inferential results with those obtained via classical testing proposals. Methods under assessment are time-series regression and cross-sectional regression. The main findings indicate that the multifactor model proposed improves the Capital Asset Pricing Model with regard to the adjusted-R2 in the time-series regressions. Cross-section regression results reveal that Market and a factor related to Momentum and mean of stocks’ returns have positive risk premia for the analyzed period. Finally, we also observe that tests based on block-bootstrap statistics are more conservative with the null than classical procedures. Full article
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Article
Short-Term Exuberance and Long-Term Stability: A Simultaneous Optimization of Stock Return Predictions for Short and Long Horizons
Mathematics 2021, 9(6), 620; https://doi.org/10.3390/math9060620 - 15 Mar 2021
Viewed by 583
Abstract
The fundamental interest of investors in econometric modeling for excess stock returns usually focuses either on short- or long-term predictions to individually reduce the investment risk. In this paper, we present a new and simple model that contemporaneously accounts for short- and long-term [...] Read more.
The fundamental interest of investors in econometric modeling for excess stock returns usually focuses either on short- or long-term predictions to individually reduce the investment risk. In this paper, we present a new and simple model that contemporaneously accounts for short- and long-term predictions. By combining the different horizons, we exploit the lower long-term variance to further reduce the short-term variance, which is susceptible to speculative exuberance. As a consequence, the long-term pension-saver avoids an over-conservative portfolio with implied potential upside reductions given their optimal risk appetite. Different combinations of short and long horizons as well as definitions of excess returns, for example, concerning the traditional short-term interest rate but also the inflation, are easily accommodated in our model. Full article
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Article
RiskLogitboost Regression for Rare Events in Binary Response: An Econometric Approach
Mathematics 2021, 9(5), 579; https://doi.org/10.3390/math9050579 - 09 Mar 2021
Viewed by 462
Abstract
A boosting-based machine learning algorithm is presented to model a binary response with large imbalance, i.e., a rare event. The new method (i) reduces the prediction error of the rare class, and (ii) approximates an econometric model that allows interpretability. RiskLogitboost regression includes [...] Read more.
A boosting-based machine learning algorithm is presented to model a binary response with large imbalance, i.e., a rare event. The new method (i) reduces the prediction error of the rare class, and (ii) approximates an econometric model that allows interpretability. RiskLogitboost regression includes a weighting mechanism that oversamples or undersamples observations according to their misclassification likelihood and a generalized least squares bias correction strategy to reduce the prediction error. An illustration using a real French third-party liability motor insurance data set is presented. The results show that RiskLogitboost regression improves the rate of detection of rare events compared to some boosting-based and tree-based algorithms and some existing methods designed to treat imbalanced responses. Full article
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Article
Multivariate Classes of GB2 Distributions with Applications
Mathematics 2021, 9(1), 72; https://doi.org/10.3390/math9010072 - 31 Dec 2020
Cited by 3 | Viewed by 663
Abstract
The general beta of the second kind distribution (GB2) is a flexible distribution which includes several relevant parametric families of distributions. This distribution has important applications in earnings and income distributions, finance and insurance. In this paper, several multivariate classes of the GB2 [...] Read more.
The general beta of the second kind distribution (GB2) is a flexible distribution which includes several relevant parametric families of distributions. This distribution has important applications in earnings and income distributions, finance and insurance. In this paper, several multivariate classes of the GB2 distribution are proposed. The different multivariate versions are based on two simple univariate representations of the GB2 distribution. The first type of multivariate distributions are constructed from a stochastic dependent representations defined in terms of gamma random variables. Using this representation and beginning by two particular multivariate GB2 distributions, multivariate Singh–Maddala and Dagum income distributions are presented and several properties are obtained. Then, a general multivariate GB2 distribution is introduced. The second type of multivariate distributions are based on a generalization of the distribution of the order statistics, which gives place to multivariate GB2 distribution with support above the diagonal. We discuss the role of these families in modeling bivariate income distributions. Finally, an empirical application is given, where we show that a multivariate GB2 distribution can be useful for modeling compound precipitation and wind events in the whole range. Full article
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Article
Modeling the Conditional Dependence between Discrete and Continuous Random Variables with Applications in Insurance
Mathematics 2021, 9(1), 45; https://doi.org/10.3390/math9010045 - 28 Dec 2020
Viewed by 468
Abstract
We jointly model amount of expenditure for outpatient visits and number of outpatient visits by considering both dependence and simultaneity by proposing a bivariate structural model that describes both variables, specified in terms of their conditional distributions. For that reason, we assume that [...] Read more.
We jointly model amount of expenditure for outpatient visits and number of outpatient visits by considering both dependence and simultaneity by proposing a bivariate structural model that describes both variables, specified in terms of their conditional distributions. For that reason, we assume that the conditional expectation of expenditure for outpatient visits with respect to the number of outpatient visits and also, the number of outpatient visits expectation with respect to the expenditure for outpatient visits is related by taking a linear relationship for these conditional expectations. Furthermore, one of the conditional distributions obtained in our study is used to derive Bayesian premiums which take into account both the number of claims and the size of the correspondent claims. Our proposal is illustrated with a numerical example based on data of health care use taken from Medical Expenditure Panel Survey (MEPS), conducted by the U.S. Agency of Health Research and Quality. Full article
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Article
Adaptive Bernstein Copulas and Risk Management
Mathematics 2020, 8(12), 2221; https://doi.org/10.3390/math8122221 - 14 Dec 2020
Cited by 1 | Viewed by 514 | Correction
Abstract
We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort [...] Read more.
We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas regarding the estimation of risk measures in risk management. Full article
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Article
Generalized Market Uncertainty Measurement in European Stock Markets in Real Time
Mathematics 2020, 8(12), 2148; https://doi.org/10.3390/math8122148 - 02 Dec 2020
Viewed by 545
Abstract
We estimate generalized market uncertainty indicators for the stock markets of eight European countries greatly affected by the recent Covid-19 crisis and the economic measures implemented for its containment and mitigation. Our statistics emphasize the difference between risk and uncertainty, in the aggregate, [...] Read more.
We estimate generalized market uncertainty indicators for the stock markets of eight European countries greatly affected by the recent Covid-19 crisis and the economic measures implemented for its containment and mitigation. Our statistics emphasize the difference between risk and uncertainty, in the aggregate, and provide readily and easily interpretable estimates, in real time, which are relevant for market participants and regulators. We show that generalized uncertainty in Europe was, indeed, at historically high levels in the wake of the recent public health crisis before the large interventions by the European Central Bank, the Fed, and the Bank of England, but also that, for some markets, recently recorded uncertainty levels were still lower than those recorded during the Global Financial Crisis, which puts things into perspective. We also show that uncertainty shocks are extremely persistent, but such persistence varies greatly across countries. The period needed for the markets to absorb half of the shock lies between less than a year and two and a half years. Full article
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Article
Portfolio Risk Assessment under Dynamic (Equi)Correlation and Semi-Nonparametric Estimation: An Application to Cryptocurrencies
Mathematics 2020, 8(12), 2110; https://doi.org/10.3390/math8122110 - 26 Nov 2020
Cited by 3 | Viewed by 633
Abstract
The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to [...] Read more.
The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of dynamic equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio of cryptocurrencies by implementing backtesting techniques and for different risk measures: value-at-risk, expected shortfall and median shortfall. The results support our proposal showing that the SNP-DCC model has better performance for lower confidence levels than the SNP-DECO model and is more appropriate for portfolio diversification purposes. Full article
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Article
Longer-Term Forecasting of Excess Stock Returns—The Five-Year Case
Mathematics 2020, 8(6), 927; https://doi.org/10.3390/math8060927 - 05 Jun 2020
Cited by 2 | Viewed by 871
Abstract
Long-term return expectations or predictions play an important role in planning purposes and guidance of long-term investors. Five-year stock returns are less volatile around their geometric mean than returns of higher frequency, such as one-year returns. One would, therefore, expect models using the [...] Read more.
Long-term return expectations or predictions play an important role in planning purposes and guidance of long-term investors. Five-year stock returns are less volatile around their geometric mean than returns of higher frequency, such as one-year returns. One would, therefore, expect models using the latter to better reduce the noise and beat the simple historical mean than models based on the former. However, this paper shows that the general tendency is surprisingly the opposite: long-term forecasts over five years have a similar or even better predictive power when compared to the one-year case. We consider a long list of economic predictors and benchmarks relevant for the long-term investor. Our predictive approach consists of adopting and implementing a fully nonparametric smoother with the covariates and the smoothing parameters chosen by cross-validation. We consistently find that long-term forecasting performs well and recommend drawing more attention to it when designing investment strategies for long-term investors. Furthermore, our preferred predictive model did stand the test of Covid-19 providing a relatively optimistic outlook in March 2020 when uncertainty was all around us with lockdown and facing an unknown new pandemic. Full article
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