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Title:

Copula structure analysis

Description:

We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation-like structure remains, but differe...

We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behaviour of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copula-based approach and the classical approach. Our new method yielear models also. Copyright Journal compilation (c) 2009 Royal Statistical Society. Minimize

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Title:

Optimal portfolios when stock prices follow an exponential Lévy process

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We investigate some portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the risk, where we measure risk by the variance, but also by the Capital-at-Risk (CaR). The solution of the mean-variance problem has the same structure for any price process which follows an exponential Lévy proc...

We investigate some portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the risk, where we measure risk by the variance, but also by the Capital-at-Risk (CaR). The solution of the mean-variance problem has the same structure for any price process which follows an exponential Lévy process. The CaR involves a quantile of the corresponding wealth process of the portfolio. We derive a weak limit law for its approximation by a simpler Lévy process, often the sum of a drift term, a Brownian motion and a compound Poisson process. Certain relations between a Lévy process and its stochastic exponential are investigated. Copyright Springer-Verlag Berlin/Heidelberg 2004 ; Capital-at-risk, downside risk measure, exponential Lévy process, portfolio optimization, stochastic exponential, Value-at-Risk, weak limit law for Lévy processes. Minimize

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Title:

A geometric approach to portfolio optimization in models with transaction costs

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We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique visc...

We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique viscosity solution of a HJB equation. Copyright Springer-Verlag Berlin/Heidelberg 2004 ; Currency market, transaction costs, consumption-investment problem, utility function, HJB equation, viscosity solution Minimize

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Title:

Subexponential Distributions - Large Deviations with Applications to Insurance and Queueing Models

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article

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Title:

High-level dependence in time series models

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We present several notions of high-level dependence for stochastic processes, which have appeared in the literature. We calculate such measures for discrete and continuous-time models, where we concentrate on time series with heavy-tailed marginals, where extremes are likely to occur in clusters. Such models include linear models and solutions t...

We present several notions of high-level dependence for stochastic processes, which have appeared in the literature. We calculate such measures for discrete and continuous-time models, where we concentrate on time series with heavy-tailed marginals, where extremes are likely to occur in clusters. Such models include linear models and solutions to random recurrence equations; in particular, discrete and continuous-time moving average and (G)ARCH processes. To illustrate our results we present a small simulation study. Minimize

Publisher:

Springer US

Year of Publication:

2010-03-01

Source:

Extremes, 2010-03-01, Volume 13, pp 1-33

Extremes, 2010-03-01, Volume 13, pp 1-33 Minimize

Language:

En

Subjects:

ARCH ; COGARCH ; Extreme cluster ; Extreme dependence measure ; Extremal index ; Extreme value theory ; GARCH ; Linear model ; Multivariate regular variation ; Nonlinear model ; Lévy-driven Ornstein–Uhlenbeck process ; Random recurrence equation ; 60G70 ; 62G32 ; 62M10

ARCH ; COGARCH ; Extreme cluster ; Extreme dependence measure ; Extremal index ; Extreme value theory ; GARCH ; Linear model ; Multivariate regular variation ; Nonlinear model ; Lévy-driven Ornstein–Uhlenbeck process ; Random recurrence equation ; 60G70 ; 62G32 ; 62M10 Minimize

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Title:

Semi-Parametric Models for the Multivariate Tail Dependence Function - the Asymptotically Dependent Case

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In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high-dimensional vector after standardizing marginals. Hence, it is of importance to model and estimate tail dependence functions. Even for moderate dimension, non-parametrically estimating a tail dependence fun...

In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high-dimensional vector after standardizing marginals. Hence, it is of importance to model and estimate tail dependence functions. Even for moderate dimension, non-parametrically estimating a tail dependence function is very inefficient and fitting a parametric model to tail dependence functions is not robust. In this paper, we propose a semi-parametric model for (asymptotically dependent) tail dependence functions via an elliptical copula. Under this model assumption, we propose a novel estimator for the tail dependence function, which proves favourable compared to the empirical tail dependence function estimator, both theoretically and empirically. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008. Minimize

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Title:

Optimal Portfolios with Bounded Capital at Risk

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Title:

Developments in Insurance Mathematics

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. Insurance mathematics in the 1990s has been influenced firstly, by the increase of catastrophic claims which had already become apparent during the early seventies and eighties and required new mathematical and statistical methods and, secondly, by a fast increasing financial market that is interested in new investment possibilities. Ideas fro...

. Insurance mathematics in the 1990s has been influenced firstly, by the increase of catastrophic claims which had already become apparent during the early seventies and eighties and required new mathematical and statistical methods and, secondly, by a fast increasing financial market that is interested in new investment possibilities. Ideas from extreme value theory and mathematical finance have been introduced into insurance mathematics and enriched classical insurance methods. But the exchange is not only from mathematical finance to insurance mathematics. The continuing occurrence of crashes in the financial market has led to a new development in mathematical finance: models and tools from insurance mathematics have entered the world of finance. This paper presents examples, both from the insurance and the finance world. The choice of topics is guided by personal taste and my own work. 1 Introduction The profession of the actuary is one of the oldest in the financial world. It st. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

http://www-m1.mathematik.tu-muenchen.de/m4/Papers/Klueppelberg/ins000415.ps.gz

http://www-m1.mathematik.tu-muenchen.de/m4/Papers/Klueppelberg/ins000415.ps.gz Minimize

Document Type:

text

Language:

en

DDC:

190 Modern western philosophy *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Optimal Portfolios When Stock Prices Follow an Exponential Lévy Process

Description:

We investigate some portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the risk, where we measure risk by the variance, but also by the Capital-at-Risk (CaR). The solution of the mean-variance problem has the same structure for any price process which follows an exponential Levy proc...

We investigate some portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the risk, where we measure risk by the variance, but also by the Capital-at-Risk (CaR). The solution of the mean-variance problem has the same structure for any price process which follows an exponential Levy process. The CaR involves a quantile of the corresponding wealth process of the portfolio. We derive a weak limit law for its approximation by a simpler Levy process, often the sum of a drift term, a Brownian motion and a compound Poisson process. Certain relations between a Levy process and its stochastic exponential are investigated. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-18

Source:

http://www-lit.ma.tum.de/veroeff/quel/029.60015.ps.gz

http://www-lit.ma.tum.de/veroeff/quel/029.60015.ps.gz Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

A Geometric Approach to Portfolio Optimization in Models With Transaction Costs

Description:

We consider a continuous-time stochastic optimization problem with in nite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique visco...

We consider a continuous-time stochastic optimization problem with in nite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique viscosity solution of a HJB equation. Mathematics Subject Classi cation (2000): 60G44 JEL Classi cation Numbers: G13, G11 Keywords: currency market, transaction cost, consumption-investment problem, utility function, HJB equation, viscosity solution. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-18

Source:

http://www-lit.ma.tum.de/veroeff/quel/029.60010.ps.gz

http://www-lit.ma.tum.de/veroeff/quel/029.60010.ps.gz Minimize

Document Type:

text

Language:

en

Subjects:

JEL Classication Numbers ; G13 ; G11 Keywords ; currency market ; transaction cost ; consumption-investment problem ; utility function ; HJB equation ; viscosity solution

JEL Classication Numbers ; G13 ; G11 Keywords ; currency market ; transaction cost ; consumption-investment problem ; utility function ; HJB equation ; viscosity solution Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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