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Papers by Zinoviy Landsman

Research paper thumbnail of Multivariate Families with Mixture Dependence

Research paper thumbnail of A Multivariate Tail Covariance Measure for Elliptical Distributions

Social Science Research Network, 2017

Research paper thumbnail of Random volatility and option prices with the generalized Student-t distribution

Advances and applications in statistics, 2006

ABSTRACT

Research paper thumbnail of A New Class of Generalised Hyper-Elliptical Distributions and Their Applications in Computing Conditional Tail Risk Measures

Social Science Research Network, 2020

This paper introduces a new family of Generalized Hyper-Elliptical (GHE) distributions providing ... more This paper introduces a new family of Generalized Hyper-Elliptical (GHE) distributions providing further generalization of the generalized hyperbolic (GH) family of distributions, considered in Ignatieva and Landsman. The GHE family is constructed by mixing a Generalized Inverse Gaussian (GIG) distribution with an elliptical distribution. We present an innovative theoretical framework where a closed form expression for the tail conditional expectation (TCE) is derived for this new family of distributions. We demonstrate that the GHE family is especially suitable for a heavy - tailed insurance losses data. Our theoretical TCE results are verified for two special cases, Laplace - GIG and Student-t - GIG mixtures. Both mixtures are shown to outperform the GH distribution providing excellent fit to univariate and multivariate insurance losses data. The TCE risk measure computed for the GHE family of distributions provides a more conservative estimator of risk in the extreme tail, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from extreme losses. Our multivariate analysis allows to quantify correlated risks by means of the GHE family: the TCE of the portfolio is decomposed into individual components, representing individual risks in the aggregate loss.

Research paper thumbnail of Stein’s Lemma for generalized skew-elliptical random vectors

Communications in Statistics, Oct 23, 2019

Research paper thumbnail of Statistical meaning of Carlen's superadditivity of the Fisher information

Statistics & Probability Letters, Mar 1, 1997

In Carlen (1991) a property of the Fisher information called “superadditivity”, was proved via an... more In Carlen (1991) a property of the Fisher information called “superadditivity”, was proved via analytic means.We show that the superadditivity is a corollary of the following simple statistical principle which is of an independent interest. The Fisher information about a parameter θ contained in an observation X = (Y,Z) with a density f(y − θ,z) is never less than the

Research paper thumbnail of Asymptotic behavior of the fisher information contained in additive statistics

Research paper thumbnail of Asymptotic tests for mean location on manifolds

Comptes Rendus De L Academie Des Sciences Serie I-mathematique, 1996

ABSTRACT

Research paper thumbnail of Relation between the covariance and Fisher information matrices

Statistics & Probability Letters, Mar 1, 1999

It is proved that for any two positive definite Hermitian m×m matrices I and V subject to I⩾V−1th... more It is proved that for any two positive definite Hermitian m×m matrices I and V subject to I⩾V−1there exists an m-variate random vector X with V as its covariance matrix and I its matrix of Fisher information.

Research paper thumbnail of Estimating the Tails of Loss Severity via Conditional Risk Measures for the Family of Symmetric Generalised Hyperbolic Family

Social Science Research Network, 2015

Research paper thumbnail of The Tail Stein's Identity with Applications to Risk Measures

The North American Actuarial Journal, Oct 1, 2016

In this article, we examine a generalized version of an identity made famous by Stein, who constr... more In this article, we examine a generalized version of an identity made famous by Stein, who constructed the so-called Stein's Lemma in the special case of a normal distribution. Other works followed to extend the lemma to the larger class of elliptical distributions. The lemma has had many applications in statistics, finance, insurance, and actuarial science. In an attempt to broaden the application of this generalized identity, we consider the version in the case where we investigate only the tail portion of the distribution of a random variable. Understanding the tails of a distribution is very important in actuarial science and insurance. Our article therefore introduces the concept of the “tail Stein's identity” to the case of any random variable defined on an appropriate probability space with a Lebesgue density function satisfying certain regularity conditions. We also examine this “tail Stein's identity” to the class of discrete distributions. This extended identity allows us to develop recursive formulas for generating tail conditional moments. As examples and illustrations, we consider several classes of distributions including the exponential family, and we apply this result to demonstrate how to generate tail conditional moments. This holds a large promise for applications in risk management.

Research paper thumbnail of Minimization of the root of a quadratic functional under a system of affine equality constraints with application in portfolio management

Research paper thumbnail of The location of a minimum variance squared distance functional

Insurance Mathematics & Economics, Jul 1, 2022

Research paper thumbnail of The Tail Stein's Identity with Actuarial Applications

Social Science Research Network, 2015

In this article, we examine a generalized version of an identity made famous by Stein (1981) who ... more In this article, we examine a generalized version of an identity made famous by Stein (1981) who constructed the so-called Stein's Lemma in the special case of a normal distribution. Other works later followed to extend the lemma to the larger class of elliptical distributions, e.g. Landsman (2006) and Landsman and Neslehova (2008). The lemma has had many applications in statistics, finance, insurance and actuarial science. In an attempt to broaden the application of this generalized identity, we consider the version in the case where we investigate only the tail portion of the distribution of a random variable. Understanding the tails of a distribution is widely important in actuarial science and insurance. Our paper therefore introduces the concept of the "tail Stein's identity" to the case of any random variable defined on an appropriate probability space with a Lebesque density function satisfying certain regularity conditions. We also examined this "tail Stein's identity" to the class of discrete distributions. This extended identity allowed us to develop recursive formulas for generating tail conditional moments. As examples and illustrations, we consider several classes of distributions including the exponential family, and we apply this result to demonstrate how to generate tail conditional moments. This has a large promise of applications in risk management.

Research paper thumbnail of The classes of distribution families with the lower bound of fisher information and its meaning in the statistical estimation

Research paper thumbnail of An informational analog of the theorem of independence of sample mean and sample variance

Journal of Soviet mathematics, Feb 1, 1988

Research paper thumbnail of Conditional Tail Risk Measures for Skewed Generalised Hyperbolic Family

Social Science Research Network, 2017

Research paper thumbnail of Lifetime Dependence Modelling Using the Truncated Multivariate Gamma Distribution

Social Science Research Network, 2012

Research paper thumbnail of A class of generalised hyper-elliptical distributions and their applications in computing conditional tail risk measures

Insurance Mathematics & Economics, Nov 1, 2021

Abstract This paper introduces a new family of Generalised Hyper-Elliptical (GHE) distributions p... more Abstract This paper introduces a new family of Generalised Hyper-Elliptical (GHE) distributions providing further generalisation of the generalised hyperbolic (GH) family of distributions, considered in Ignatieva and Landsman (2019) . The GHE family is constructed by mixing a Generalised Inverse Gaussian (GIG) distribution with an elliptical distribution. We present an innovative theoretical framework where a closed form expression for the tail conditional expectation (TCE) is derived for this new family of distributions. We demonstrate that the GHE family is especially suitable for heavy-tailed insurance losses data. Our theoretical TCE results are verified for two special cases, Laplace - GIG and Student-t - GIG mixtures. Both mixtures are shown to outperform the GH distribution, providing excellent fit to univariate and multivariate insurance losses data. The TCE risk measure computed for the GHE family of distributions provides a more conservative estimator of risk in the extreme tail, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from extreme losses. Our multivariate analysis allows to quantify correlated risks by means of the GHE family: the TCE of the portfolio is decomposed into individual components, representing individual risks in the aggregate loss.

Research paper thumbnail of A New Approach to Multivariate Archimedean Copula Generation

Research paper thumbnail of Multivariate Families with Mixture Dependence

Research paper thumbnail of A Multivariate Tail Covariance Measure for Elliptical Distributions

Social Science Research Network, 2017

Research paper thumbnail of Random volatility and option prices with the generalized Student-t distribution

Advances and applications in statistics, 2006

ABSTRACT

Research paper thumbnail of A New Class of Generalised Hyper-Elliptical Distributions and Their Applications in Computing Conditional Tail Risk Measures

Social Science Research Network, 2020

This paper introduces a new family of Generalized Hyper-Elliptical (GHE) distributions providing ... more This paper introduces a new family of Generalized Hyper-Elliptical (GHE) distributions providing further generalization of the generalized hyperbolic (GH) family of distributions, considered in Ignatieva and Landsman. The GHE family is constructed by mixing a Generalized Inverse Gaussian (GIG) distribution with an elliptical distribution. We present an innovative theoretical framework where a closed form expression for the tail conditional expectation (TCE) is derived for this new family of distributions. We demonstrate that the GHE family is especially suitable for a heavy - tailed insurance losses data. Our theoretical TCE results are verified for two special cases, Laplace - GIG and Student-t - GIG mixtures. Both mixtures are shown to outperform the GH distribution providing excellent fit to univariate and multivariate insurance losses data. The TCE risk measure computed for the GHE family of distributions provides a more conservative estimator of risk in the extreme tail, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from extreme losses. Our multivariate analysis allows to quantify correlated risks by means of the GHE family: the TCE of the portfolio is decomposed into individual components, representing individual risks in the aggregate loss.

Research paper thumbnail of Stein’s Lemma for generalized skew-elliptical random vectors

Communications in Statistics, Oct 23, 2019

Research paper thumbnail of Statistical meaning of Carlen's superadditivity of the Fisher information

Statistics & Probability Letters, Mar 1, 1997

In Carlen (1991) a property of the Fisher information called “superadditivity”, was proved via an... more In Carlen (1991) a property of the Fisher information called “superadditivity”, was proved via analytic means.We show that the superadditivity is a corollary of the following simple statistical principle which is of an independent interest. The Fisher information about a parameter θ contained in an observation X = (Y,Z) with a density f(y − θ,z) is never less than the

Research paper thumbnail of Asymptotic behavior of the fisher information contained in additive statistics

Research paper thumbnail of Asymptotic tests for mean location on manifolds

Comptes Rendus De L Academie Des Sciences Serie I-mathematique, 1996

ABSTRACT

Research paper thumbnail of Relation between the covariance and Fisher information matrices

Statistics & Probability Letters, Mar 1, 1999

It is proved that for any two positive definite Hermitian m×m matrices I and V subject to I⩾V−1th... more It is proved that for any two positive definite Hermitian m×m matrices I and V subject to I⩾V−1there exists an m-variate random vector X with V as its covariance matrix and I its matrix of Fisher information.

Research paper thumbnail of Estimating the Tails of Loss Severity via Conditional Risk Measures for the Family of Symmetric Generalised Hyperbolic Family

Social Science Research Network, 2015

Research paper thumbnail of The Tail Stein's Identity with Applications to Risk Measures

The North American Actuarial Journal, Oct 1, 2016

In this article, we examine a generalized version of an identity made famous by Stein, who constr... more In this article, we examine a generalized version of an identity made famous by Stein, who constructed the so-called Stein's Lemma in the special case of a normal distribution. Other works followed to extend the lemma to the larger class of elliptical distributions. The lemma has had many applications in statistics, finance, insurance, and actuarial science. In an attempt to broaden the application of this generalized identity, we consider the version in the case where we investigate only the tail portion of the distribution of a random variable. Understanding the tails of a distribution is very important in actuarial science and insurance. Our article therefore introduces the concept of the “tail Stein's identity” to the case of any random variable defined on an appropriate probability space with a Lebesgue density function satisfying certain regularity conditions. We also examine this “tail Stein's identity” to the class of discrete distributions. This extended identity allows us to develop recursive formulas for generating tail conditional moments. As examples and illustrations, we consider several classes of distributions including the exponential family, and we apply this result to demonstrate how to generate tail conditional moments. This holds a large promise for applications in risk management.

Research paper thumbnail of Minimization of the root of a quadratic functional under a system of affine equality constraints with application in portfolio management

Research paper thumbnail of The location of a minimum variance squared distance functional

Insurance Mathematics & Economics, Jul 1, 2022

Research paper thumbnail of The Tail Stein's Identity with Actuarial Applications

Social Science Research Network, 2015

In this article, we examine a generalized version of an identity made famous by Stein (1981) who ... more In this article, we examine a generalized version of an identity made famous by Stein (1981) who constructed the so-called Stein's Lemma in the special case of a normal distribution. Other works later followed to extend the lemma to the larger class of elliptical distributions, e.g. Landsman (2006) and Landsman and Neslehova (2008). The lemma has had many applications in statistics, finance, insurance and actuarial science. In an attempt to broaden the application of this generalized identity, we consider the version in the case where we investigate only the tail portion of the distribution of a random variable. Understanding the tails of a distribution is widely important in actuarial science and insurance. Our paper therefore introduces the concept of the "tail Stein's identity" to the case of any random variable defined on an appropriate probability space with a Lebesque density function satisfying certain regularity conditions. We also examined this "tail Stein's identity" to the class of discrete distributions. This extended identity allowed us to develop recursive formulas for generating tail conditional moments. As examples and illustrations, we consider several classes of distributions including the exponential family, and we apply this result to demonstrate how to generate tail conditional moments. This has a large promise of applications in risk management.

Research paper thumbnail of The classes of distribution families with the lower bound of fisher information and its meaning in the statistical estimation

Research paper thumbnail of An informational analog of the theorem of independence of sample mean and sample variance

Journal of Soviet mathematics, Feb 1, 1988

Research paper thumbnail of Conditional Tail Risk Measures for Skewed Generalised Hyperbolic Family

Social Science Research Network, 2017

Research paper thumbnail of Lifetime Dependence Modelling Using the Truncated Multivariate Gamma Distribution

Social Science Research Network, 2012

Research paper thumbnail of A class of generalised hyper-elliptical distributions and their applications in computing conditional tail risk measures

Insurance Mathematics & Economics, Nov 1, 2021

Abstract This paper introduces a new family of Generalised Hyper-Elliptical (GHE) distributions p... more Abstract This paper introduces a new family of Generalised Hyper-Elliptical (GHE) distributions providing further generalisation of the generalised hyperbolic (GH) family of distributions, considered in Ignatieva and Landsman (2019) . The GHE family is constructed by mixing a Generalised Inverse Gaussian (GIG) distribution with an elliptical distribution. We present an innovative theoretical framework where a closed form expression for the tail conditional expectation (TCE) is derived for this new family of distributions. We demonstrate that the GHE family is especially suitable for heavy-tailed insurance losses data. Our theoretical TCE results are verified for two special cases, Laplace - GIG and Student-t - GIG mixtures. Both mixtures are shown to outperform the GH distribution, providing excellent fit to univariate and multivariate insurance losses data. The TCE risk measure computed for the GHE family of distributions provides a more conservative estimator of risk in the extreme tail, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from extreme losses. Our multivariate analysis allows to quantify correlated risks by means of the GHE family: the TCE of the portfolio is decomposed into individual components, representing individual risks in the aggregate loss.

Research paper thumbnail of A New Approach to Multivariate Archimedean Copula Generation