Heavy-Tailed Distributions and Robustness in Economics and Finance

Ibragimov, M. Dzh.; Ибрагимов, Рустам; Waldén, Johan

doi:10.1007/978-3-319-16877-7

Cited by 116 publications

(92 citation statements)

References 132 publications

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“…Remark 4.1 The bounds presented in Theorem 4.1 hold for arbitrary two fixed moments of the returns of order higher than one; the moments fixed do not have to be, e.g., the mean and variance of the returns. In particular, the bounds hold for assets with heavy-tailed distributions typically observed in economic, financial and insurance markets (see, for instance, the reviews and results in Gabaix, 2008, Ibragimov, 2009, Ibragimov, Ibragimov and Walden, 2015and Ibragimov and Prokhorov, 2016 including the infinite fourth moment and even the infinite variance case.…”

Section: The Functionmentioning

confidence: 95%

“…The analysis of preferences over payoff distributions and the effects of skewness and other higher moments (e.g., kurtosis) in this framework may also relate to applications of majorization theory (seeMarshall, Olkin and Arnold, 2011) and heavy-tailed distributions (see, among othersEmbrechts, Klüuppelberg and Mikosch, 1997;Gabaix, 2008;Ibragimov, 2009;Ibragimov, Ibragimov and Walden, 2015;Ibragimov and Prokhorov, 2016).…”

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confidence: 99%

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Bounds for path-dependent options

2015

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We develop new semiparametric bounds on the expected payoffs and prices of European call options and a wide range of path-dependent contingent claims. We first focus on the trinomial financial market model in which, as is well-known, an exact calculation of derivative prices based on no-arbitrage arguments is impossible. We show that the expected payoff of a European call option in the trinomial model with martingale-difference log-returns is bounded from above by the expected payoff of a call option written on an asset with i.i.d. symmetric two-valued log-returns. We further show that the expected payoff of a European call option in the multiperiod trinomial option pricing model is bounded by the expected payoff of a call option in the two-period model with a log-normal asset price. We also obtain bounds on the possible prices of call options in the (incomplete) trinomial model in terms of the parameters of the asset's distribution. Similar bounds also hold for many other contingent claims in the trinomial option pricing model, including those with an arbitrary convex increasing payoff function as well as for path-dependent ones such as Asian options.We further obtain a wide range of new semiparametric moment bounds on the expected payoffs and prices of path-dependent Asian options with an arbitrary distribution of the underlying asset's price. These results are based on recently obtained sharp moment inequalities for sums of multilinear forms and U −statistics and provide their first financial and economic applications in the literature. Similar bounds also hold for many other path-dependent contingent claims.

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Section: The Functionmentioning

confidence: 95%

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confidence: 99%

Bounds for path-dependent options

2015

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“…The log-likelihood function can be maximized either directly or by solving the nonlinear likelihood equation obtained by differentiating (13). We used the goodness of fit function in R with "L-BFGS-B" algorithm to obtain the MLEs.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…Speaking broadly, modeling insurance loss data with a heavy tail is a prominent research topic. Insurance loss data are positive, for detail see , and their distribution is often unimodal shaped, for example see Cooray and Ananda (2005), right-skewed, for detail see Lane (2000), Vernic (2006) Kazemi and Noorizadeh (2015) and Adcock et al (2015), and with heavy tails, see Ibragimov et al (2015). Actuaries are often interested in distributions that offer data modeling with heavy tail and provide a good estimate of the associated business risk level.…”

Section: Introductionmentioning

confidence: 99%

A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

Ahmad¹,

Mahmoudi²,

Hamedani³

2019

Pak.j.stat.oper.res.

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Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.

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“…Lévy statistics applies to the description of a particular class of random walks obeying a 'heavy-tailed' probability distribution with power law dependence [1]. Lévy statistics has been studied in great details owing to its importance in numerous scientific areas where such random walks can occur, and where the long tail of Lévy distributions is essential for the prediction of rare events, be that in chemistry [2], biology [3], or in economics [4,5]. In physics, Lévy statistics appears often as a result of a complex dynamics, in various transport processes of heat, sound, or light diffusions, in chaotic systems, and in laser cooling where it has broad applications for subrecoil cooling techniques [1,[6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Lévy statistics of interacting Rydberg gases

et al. 2017

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A statistical analysis of the laser excitation of cold and randomly distributed atoms to Rydberg states is developed. We first demonstrate with a hard ball model that the distribution of energy level shifts in an interacting gas obeys Lévy statistics, in any dimension d and for any interaction −Cp/R p under the condition d/p < 1. This result is confirmed with a Monte Carlo rate equations simulation of the actual laser excitation in the particular case p = 6 and d = 3. With this finding, we develop a statistical approach for the modeling of probe light transmission through a cold atom gas driven under conditions of electromagnetically induced transparency involving a Rydberg state. The simulated results are in good agreement with experiment.

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Heavy-Tailed Distributions and Robustness in Economics and Finance

Cited by 116 publications

References 132 publications

Bounds for path-dependent options

Bounds for path-dependent options

A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

Lévy statistics of interacting Rydberg gases

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