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## Modelling dependence between Levy processes

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In this paper, we introduce a principally new method for modelling the dependence structure between two L{\'e}vy processes. The proposed method is based on some special properties of the time-changed Levy processes and can be viewed as an reasonable alternative to the copula approach.

М.: ИППИ РАН, 2013

Added: September 23, 2013

Rudenko V., Обозрение прикладной и промышленной математики 2017 Vol. 24 No. 4 P. 380-381

We analyze an impact of the dependence degree between the error components on parameters estimation in stochastic frontier model. It is also demonstrated that for derivation of estimates of technical efficiency one is advised to consider different copulas to model joint distribution of the error components. ...

Added: January 23, 2018

Ацканов И. А., Прикладная эконометрика 2015 Т. 4 № 40 С. 84-105

This paper proposes a procedure for dynamic optimization of an investment portfolio, consisting of stock market indices. SJC-copulas were used to assets statistical characteristics of assets. Copulas allow to measure interdependence between financial instruments, and to build an efficient investment portfolio. Since statistical characteristics of assets are changing with time, the structure of the portfolio ...

Added: February 3, 2016

Lubashevsky I., The European Physical Journal B 2010 Vol. 82 P. 189-195

A continuous Markovian model for truncated Lévy flights is proposed. It generalizes the approach developed previously by Lubashevsky et al. [Phys. Rev. E 79, 011110 (2009); Phys. Rev. E 80, 031148 (2009), Eur. Phys. J. B 78, 207 (2010)] and allows for nonlinear friction in wandering particle motion as well as saturation of the noise intensity ...

Added: November 6, 2021

Manita A., , in: New trends in Stochastic Modeling and Data Analysis. .: Athens: ISAST: International Society for the Advancement of Science and Technology, 2015..

Added: June 20, 2017

Belomestny D., Panov V., Electronic journal of statistics 2015 Vol. 9 No. 2 P. 1974-2006

In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type
\[
X_{t} = e^{-\xi_{t}} \left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right),
\]
where \(\xi_s\) is a L{\'e}vy process. Our primal goal is to estimate the characteristics of the L\'evy process \(\xi\) from the low-frequency observations of the process \(X\). We present ...

Added: September 1, 2015

Lubashevsky I., Heuer A., Friedrich R. et al., The European Physical Journal B 2010 Vol. 78 P. 207-216

We consider a previously devised model describing Lévy random walks [I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 79, 011110 (2009); I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 80, 031148 (2009)]. It is demonstrated numerically that the given model describes Lévy random walks with superdiffusive, ballistic, as well as superballistic dynamics. Previously ...

Added: November 6, 2021

Penikas H. I., Прикладная эконометрика 2011 № 2 С. 3-21

The article deals with the issue of copula use in the program of price risk hedging. Copula-models performance is compared to the OLS-based ones. Fully parametric and semi-parametric approaches to copula-modeling are compared. The copula-based models efficiency is illustrated by the fact of decreasing the daily profit-and-loss volatility of the hedged portfolio by simultaneously augmenting ...

Added: September 23, 2012

Ханьков И. О., Penikas H. I., Modelling Probability of Default of Russian Banks and Companies Using Copula Models / . 2015. No. 113.

Research is devoted to examination of the classifier, based on copula discriminant analysis (CODA). Performance of the classification of this algorithm was assessed. On samples, modelled with some typical features of corporate default data, sensitivity of the classifier was tested, to sample size, to default rate and to different patterns of variables’ interdependence. Alternative copula ...

Added: January 11, 2016

Manita A., Journal of Physics: Conference Series 2016 Vol. 681 No. 1 P. 1-6

We consider N-component synchronization models defined in terms of stochastic particle systems with special interaction. For general (nonsymmetric) Markov models we discuss phenomenon of the long time stochastic synchronization. We study behavior of the system in different limit situations related to appropriate changes of variables and scalings. For N = 2 limit distributions are found ...

Added: March 29, 2016

Gushchin A. A., Kordzakhia N., Novikov A. A., Statistical Inference for Stochastic Processes 2018 Vol. 21 No. 2 P. 363-383

We provide a full description of the class of translation invariant experiments with independent increments. Necessary and sufficient conditions for the weak convergence and the comparison of experiments within this class are given. Finally, we prove exponential boundedness of Pitman estimators in these models. ...

Added: June 29, 2018

Belomestny D., GUGUSHVILI S., SCHAUER M. et al., Communications in Mathematical Sciences 2019 Vol. 17 No. 3 P. 781-816

Given discrete time observations over a growing time interval, we consider a nonparametric Bayesian approach to estimation of the Levy density of a Levy process belonging to a flexible class of infinite activity subordinators. Posterior inference is performed via MCMC, and we circumvent the problem of the intractable likelihood via the data augmentation device, that ...

Added: June 11, 2019

Ayvazyan S. A., Andrievskaya I. K., Penikas H. I. et al., Review of Applied Socio-Economic Research 2011 Vol. 1 No. 1 P. 70-80

The world financial crisis of 2008-2009 has shown that the existence of systemically important financial institutions (SIFIs) poses serious policy challenges to both developed and developing economies’ authorities. As for now there are different approaches to identifying SIFIs focused on contagion, concentration, correlation and conditions effects. The paper aims at testing a new approach to ...

Added: November 3, 2013

Merikas A., Merika A., Penikas H. I., , in: Многомерный статистический анализ и эконометрика. Труды VIII Международной школы-семинара. .: Цахкадзор: ЦЭМИ РАН, 2012.. P. 178-180.

The objective of the research is to study the properties of joint distribution of returns for dry bulk time charter rates and to find out the more efficient time series model describing their dynamics with respect to goodness-of-forecasting. ...

Added: July 9, 2012

Penikas H. I., Andrievskaya I. K., Model Assisted Statistics and Applications 2012 Vol. 7 No. 4 P. 267-280

According to the strategy of the banking system development until 2015, the Central Bank of Russia is going to implement Basel II Internal-Ratings-Based (IRB) approaches in 2015, while Basel III is planned to be introduced in full starting from 2019. Taking into account the effects of the Basel II regulation during the crisis 2008-2009, in ...

Added: November 6, 2012

Lakshina V. V., Экономический журнал Высшей школы экономики 2016 Т. 20 № 1 С. 156-174

This paper studies the problem of calculation the dynamic hedge ratio for the portfolio consisted of two assets. Commonly it’s solved assuming that the investor’s risk aversion is infinite. Then the optimal hedge coefficient is equal to ratio of covariance of the hedged and hedging assets to the variance of the latter. It’s natural to ...

Added: October 15, 2015

Belomestny D., Comte F., Genon-Catalot V. et al., Heidelberg: Springer, 2014

...

Added: December 12, 2014

Finkelstein D., Kondratiev Y., Molchanov S. et al., Stochastics and Dynamics 2018 Vol. 18 No. 05 P. 1850037

We study stability of stationary solutions for a class of nonlocal semilinear parabolic equations. To this end, we prove the Feynman–Kac formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the zero solution, and use them to the study of the spatial logistic equation ...

Added: November 14, 2019

Penikas H. I., Журнал Новой экономической ассоциации 2010 № 7 С. 24-44

The paper aims at introducing copula-models' concepts and its application to solving such financials programs as risk measurement, risk hedging, portfolio optimization, derivatives pricing and duration models evaluation. For the purpose the copula definition is firstly introduced. Then different copula families, model estimation and inference techniques are discussed. A detailed review of relevant literature is ...

Added: November 6, 2012

Merikas A., Merika A., Penikas H. I., Procedia Computer Science 2013 Vol. 17 P. 1125-1133

The paper is the first to the knowledge of the authors to apply copula models to reconstructing joint distribution of time charter rates for dry bulk ship. Based on the Clarksons dataset for the last 20 years it is claimed that Gumbel copula is enough to perform the mentioned objective. To arrive at the conclusion ...

Added: June 11, 2013

Lubashevsky I., Physica A: Statistical Mechanics and its Applications 2013 Vol. 392 No. 10 P. 2323-2346

The paper is devoted to the relationship between the continuous Markovian description of Lévy flights developed previously (see, e.g., I.A. Lubashevsky, Truncated Lévy flights and generalized Cauchy processes, Eur. Phys. J. B 82 (2011) 189–195 and references therein) and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of ...

Added: November 6, 2021

Belomestny D., Orlova T., Panov V., Statistical inference for moving-average Lévy-driven processes: Fourier-based approach / . 2017. No. 1702.02794.

We consider a new method of the semiparametric statistical estimation for the continuous-time moving average L\'evy processes. We derive the convergence rates of the proposed estimators, and show that these rates are optimal in the minimax sense. ...

Added: February 10, 2017

Manita A., Journal of Physics: Conference Series 2019 Vol. 1163 No. 012060 P. 1-7

L´evy stochastic processes and related fine analytic properties of probability distributions such as infinite divisibility play an important role in construction of stochastic models of various distributed networks (e.g., local clock synchronization), of some physical systems (e.g., anomalous diffusions, quantum probability models), of finance etc. Nevertheless, little is known about limit probability laws resulted from ...

Added: June 21, 2019

Kelbert M., Moreno-Franco H. A., SIAM Journal on Control and Optimization 2019 Vol. 57 No. 3 P. 2185-2213

In this paper, we guarantee the existence and uniqueness (in the almost everywhere
sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient
constraint and a partial integro-di erential operator whose Levy measure has bounded
variation. This type of equation arises in a singular control problem, where the state
process is a multidimensional jump-di usion with jumps of ...

Added: February 13, 2019