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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:

Copula structure analysis

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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:

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:

Risk Management with Extreme Value Theory

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-04-06

Source:

http://www-lit.ma.tum.de/veroeff/quel/029.60018.ps.gz

http://www-lit.ma.tum.de/veroeff/quel/029.60018.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:

The Tail of the Stationary Distribution of an Autoregressive Process with ARCH(1) Errors

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We consider the class of autoregressive processes with ARCH(1) errors given by the stochastic difference equation Xn = ffXn\Gamma1 + q fi + X 2 n\Gamma1 " n ; n 2 N ; where (" n ) n2N are i.i.d. random variables. Under general and tractable assumptions we show the existence and uniqueness of a stationary distribution. We prove that the stationar...

We consider the class of autoregressive processes with ARCH(1) errors given by the stochastic difference equation Xn = ffXn\Gamma1 + q fi + X 2 n\Gamma1 " n ; n 2 N ; where (" n ) n2N are i.i.d. random variables. Under general and tractable assumptions we show the existence and uniqueness of a stationary distribution. We prove that the stationary distribution has a Pareto-like tail with a well-specified tail index which depends on ff, and the distribution of the innovations (" n ) n2N . This paper generalizes results for the ARCH(1) process (the case ff = 0) proved by Kesten (1973), Vervaat (1979) and Goldie (1991). The generalization requires a new method of proof and we invoke a Tauberian theorem. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-11-14

Source:

http://www-m1.mathematik.tu-muenchen.de/m4/Papers/Borkovec/tail000606.ps

http://www-m1.mathematik.tu-muenchen.de/m4/Papers/Borkovec/tail000606.ps Minimize

Document Type:

text

Language:

en

Subjects:

recurrent Harris chain ; regular variation ; strong mixing ; Tauberian theorem

recurrent Harris chain ; regular variation ; strong mixing ; Tauberian theorem 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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Title:

A Single Number Can't Hedge Against Economic Catastrophes

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Mathematics and statistics have transformed the day-to-day trading in the world's financial markets. This has lead to new ways to reduce (or "hedge") risks which provides an important service to society, but also a temptation to very big gambles, with a potential for extreme losses. This paper discusses some of the ways statistics and mathematic...

Mathematics and statistics have transformed the day-to-day trading in the world's financial markets. This has lead to new ways to reduce (or "hedge") risks which provides an important service to society, but also a temptation to very big gambles, with a potential for extreme losses. This paper discusses some of the ways statistics and mathematics can be used to understand and protect against very large, "catastrophic" financial risks. We argue that means don't mean anything for catastrophic risk, that separate large financial risks often are better handled by separate companies, and that the mathematical aspects of risk can't be summarized into one number. We also believe that there is a large potential for improved risk management in financial institutions, where extreme value theory, a speciality of the present authors, may be a useful tool. Improvements, however will not come for free but require long and hard work, where mathematics is only one part of the total effort. 1 Introdu. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Klueppelberg/cat990701.ps.gz

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Klueppelberg/cat990701.ps.gz Minimize

Document Type:

text

Language:

en

DDC:

332 Financial economics *(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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