Using rotations to build non symmetric extensions of Amblard-Girard copulas

A copula is a function that completely describes the dependence structure between the marginal distributions. One of the most important para-metric family of copulas is the Farlie-Gumbel-Morgenstern (FGM) family. In practical applications this copula has been shown to be somewhat limited and a symmetric extension of this family, known as the Amblard-Girard copula, has been introduced. Basing on rotations, we propose a new non symmetric extension of this family

An extension of FGM distributions based on an univariate function

A copula is a function that completely describes the dependence structure between the marginal distributions. One of the most important para-metric family of copulas is the Farlie-Gumbel-Morgenstern (FGM) family. In practical applications this copula has been shown to be somewhat limited. We propose a new extension of this family based on the introduction of an univariate function

Survival Amblard-Girard copulas

A copula is a function that completely describes the dependence structure between the marginal distributions. One of the most important para-metric family of copulas is the Farlie-Gumbel-Morgenstern (FGM) family. In practical applications this copula has been shown to be somewhat limited and a symmetric extension of this family, known as the Amblard-Girard copula, has been introduced. The goal of this note is to prove that the survival copula associated with an Amblard-Girard copula still is an Amblard-Girard copula

Modeling Financial Return Dynamics by Decomposition

While the predictability of excess stock returns is statistically small, their sign and volatility exhibit a substantially larger degree of dependence over time. We capitalize on this observation and consider prediction of excess stock returns by decomposing the equity premium into a product of sign and absolute value components and carefully modeling the marginal predictive densities of the two parts. Then we construct the joint density of a positively valued (absolute returns) random variable and a discrete binary (sign) random variable by copula methods and discuss computation of the conditional mean predictor. Our empirical analysis of US stock return data shows among other interesting ndings that despite the large unconditional correlation between the two multiplicative components they are conditionally very weakly dependent.Stock returns predictability; Directional forecasting; Absolute returns; Joint predictive distribution; Copulas.

On the impact of asymmetric dependence in the actuarial pricing of joint life insurance policies

Multipopulation mortality modeling is a significant research problem in actuarial science. Mortality functions involving multiple lives are also essential to determine the pricing of premiums. Moreover, the lifetime models based on dependence and asymmetry are more realistic. Hence, this paper applies an asymmetric copula model, Generalized FGM (GFGM) to model the bivariate joint distribution of future lifetimes. Premiums of first-death life insurance products are calculated based on the proposed model and compared with independent and symmetrical models. The results display that asymmetry has a significant effect on premium calculations. Also, it is concluded that the lowest premiums are generally in asymmetric lifetime models. This paper also provides analytical examples for the proposed model with Gompertz’s marginal law

Copula Theory and Regression Analysis

Researchers are often interested to study in the relationships between one variable and several other variables. Regression analysis is the statistical method for investigating such relationship and it is one of the most commonly used statistical Methods in many scientific fields such as financial data analysis, medicine, biology, agriculture, economics, engineering, sociology, geology, etc. But basic form of the regression analysis, ordinary least squares is not suitable for actuarial applications because the relationships are often nonlinear and the probability distribution of the response variable may be non-Gaussian distribution. One of the method that has been successful in overcoming these challenges is the generalized linear model (GLM), which requires that the response variable have a distribution from the exponential family. In this research work, we study copula regression as an alternative method to OLS and GLM. The major advantage of a copula regression is that there are no restrictions on the probability distributions that can be used. First part of this study, we will briefly discuss about copula regression by using several variety of marginal copula functions and copula regression is the most appropriate method in non Gaussian variable(violated normality assumption) regression model fitting. Also we validated our results by using real world example data and random generated (50000 observations) data. Second part of this study, we discussed about multiple regression model based on copula theory, and also we derived multiple regression line equation for Multivariate Non-Exchangeable Generalized Farlie-Gumbel-Morgenstern (FGM) copula function

Directionally Dependent Multi-View Clustering Using Copula Model

In recent biomedical scientific problems, it is a fundamental issue to integratively cluster a set of objects from multiple sources of datasets. Such problems are mostly encountered in genomics, where data is collected from various sources, and typically represent distinct yet complementary information. Integrating these data sources for multi-source clustering is challenging due to their complex dependence structure including directional dependency. Particularly in genomics studies, it is known that there is certain directional dependence between DNA expression, DNA methylation, and RNA expression, widely called The Central Dogma. Most of the existing multi-view clustering methods either assume an independent structure or pair-wise (non-directional) dependency, thereby ignoring the directional relationship. Motivated by this, we propose a copula-based multi-view clustering model where a copula enables the model to accommodate the directional dependence existing in the datasets. We conduct a simulation experiment where the simulated datasets exhibiting inherent directional dependence: it turns out that ignoring the directional dependence negatively affects the clustering performance. As a real application, we applied our model to the breast cancer tumor samples collected from The Cancer Genome Altas (TCGA)

Quantitative Methods for Economics and Finance

This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice