Displaying similar documents to “Multivariate extensions of expectiles risk measures”

Multivariate measures of concordance for copulas and their marginals

M. D. Taylor (2016)

Dependence Modeling

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Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular,we examine the relations between the measure of concordance of an n-copula and the measures of concordance of the copula’s marginals.

Copula–Induced Measures of Concordance

Sebastian Fuchs (2016)

Dependence Modeling

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We study measures of concordance for multivariate copulas and copulas that induce measures of concordance. To this end, for a copula A, we consider the maps C → R given by [...] where C denotes the collection of all d–dimensional copulas, M is the Fréchet–Hoeffding upper bound, Π is the product copula, [. , .] : C × C → R is the biconvex form given by [C, D] := ∫ [0,1]d C(u) dQD(u) with the probability measure QD associated with the copula D, and ψΛ C → C is a transformation of copulas....

A Biconvex Form for Copulas

Sebastian Fuchs (2016)

Dependence Modeling

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We study the integration of a copula with respect to the probability measure generated by another copula. To this end, we consider the map [. , .] : C × C → R given by [...] where C denotes the collection of all d–dimensional copulas and QD denotes the probability measures associated with the copula D. Specifically, this is of interest since several measures of concordance such as Kendall’s tau, Spearman’s rho and Gini’s gamma can be expressed in terms of the map [. , .]. Quite generally,...

Forecasting time series with multivariate copulas

Clarence Simard, Bruno Rémillard (2015)

Dependence Modeling

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In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our...

On uniform tail expansions of multivariate copulas and wide convergence of measures

Piotr Jaworski (2006)

Applicationes Mathematicae

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The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for a detailed study of the tail behaviour of multivariate copulas. We investigate the class of copulas having regular tails with a uniform expansion. We present several equivalent characterizations of uniform tail expansions. Next, basing on them, we determine...

Tractability of multivariate problems for weighted spaces of functions

H. Woźniakowski (2006)

Banach Center Publications

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We survey recent results on tractability of multivariate problems. We mainly restrict ourselves to linear multivariate problems studied in the worst case setting. Typical examples include multivariate integration and function approximation for weighted spaces of smooth functions.

Bounds on integrals with respect to multivariate copulas

Michael Preischl (2016)

Dependence Modeling

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In this paper, we present a method to obtain upper and lower bounds on integrals with respect to copulas by solving the corresponding assignment problems (AP’s). In their 2014 paper, Hofer and Iacó proposed this approach for two dimensions and stated the generalization to arbitrary dimensons as an open problem. We will clarify the connection between copulas and AP’s and thus find an extension to the multidimensional case. Furthermore, we provide convergence statements and, as applications,...

Measuring herd behavior: properties and pitfalls

Woojoo Lee, Jae Youn Ahn (2017)

Dependence Modeling

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Herd behavior is an important economic phenomenon, especially in the context of the recent financial crises. Prior studies propose several measures to quantify herd behavior. In this paper, we show that these measures reflect different perspectives on this behavior, and hence, their interpretation requires great care. Taking a critical attitude toward existing herd behavior measures, we study their properties and pitfalls in detail.

Quantile hedging on markets with proportional transaction costs

Michał Baran (2003)

Applicationes Mathematicae

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The problem of risk measures in a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk are introduced. This gives a generalization of quantile hedging presented in [4].

Joint weak hazard rate order under non-symmetric copulas

Franco Pellerey, Fabio Spizzichino (2016)

Dependence Modeling

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A weak version of the joint hazard rate order, useful to stochastically compare not independent random variables, has been recently defined and studied in [4]. In the present paper, further results on this order are proved and discussed. In particular, some statements dealing with the relationships between the jointweak hazard rate order and other stochastic orders are generalized to the case of non symmetric copulas, and its relations with some multivariate aging notions (studied in...

Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances

Pierre Devolder, Adrien Lebègue (2016)

Dependence Modeling

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The purpose of this paper is twofold. First we consider a ruin theory approach along with risk measures in order to determine the solvency capital of long-term guarantees such as life insurances or pension products. Secondly, for such products,we challenge the definition of the Solvency Capital Requirement (SCR) under the Solvency II (SII) regulatory framework based on a yearly viewpoint. Several methods for the calculation of the solvency capital are presented. We start our study with...

Cost-efficiency in multivariate Lévy models

Ludger Rüschendorf, Viktor Wolf (2015)

Dependence Modeling

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In this paper we determine lowest cost strategies for given payoff distributions called cost-efficient strategies in multivariate exponential Lévy models where the pricing is based on the multivariate Esscher martingale measure. This multivariate framework allows to deal with dependent price processes as arising in typical applications. Dependence of the components of the Lévy Process implies an influence even on the pricing of efficient versions of univariate payoffs.We state various...