arXiv subjects

Sergey Kamenshchikov

Publications and source records attributed to Sergey Kamenshchikov.

8 recordsLinked to original sources

arXiv2017

Biased Risk Parity with Fractal Model of Risk

For the past two decades investors have observed long memory and highly correlated behavior of asset classes that does not fit into the framework of Modern Portfolio Theory. Custom correlation and standard deviation estimators consider normal distribution of returns and market efficiency hypothesis. It forced investors to search more universal instruments of tail risk protection. One of the possible solutions is a naive risk parity strategy, which avoids estimation of expected returns and correlations. The authors develop the idea further and propose a fractal distribution of returns as a core. This class of distributions is more general as it does not imply strict limitations on risk evolution. The proposed model allows for modifying a rule for volatility estimation, thus, enhancing its explanatory power. It turns out that the latter improves the performance metrics of an investment portfolio over the ten year period. The fractal model of volatility plays a significant protective role during the periods of market abnormal drawdowns. Consequently, it may be useful for a wide range of asset managers which incorporate innovative risk models into globally allocated portfolios.

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arXiv2016

Fractal Optimization of Market Neutral Portfolio

A fractal approach to the long-short portfolio optimization is proposed. The algorithmic system based on the composition of market-neutral spreads into a single entity was considered. The core of the optimization scheme is a fractal walk model of returns, optimizing a risk aversion according to the investment horizon. The covariance matrix of spread returns has been used for the optimization and modified according to the Hurst stability analysis. Out-of-sample performance data has been represented for the space of exchange traded funds in five period time period of observation. The considered portfolio system has turned out to be statistically more stable than a passive investment into benchmark with higher risk adjusted cumulative return over the observed period.

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arXiv2016

Bifurcation patterns of market regime transition

In this paper mechanisms of reversion - momentum transition are considered. Two basic nonlinear mechanisms are highlighted: a slow and fast bifurcation. A slow bifurcation leads to the equilibrium evolution, preceded by stability loss delay of a control parameter. A single order parameter is introduced by Markovian chain diffusion, which plays a role of a precursor. A fast bifurcation is formed by a singular fusion of unstable and stable equilibrium states. The effect of a precatastrophic range compression is observed before the discrete change of a system. A diffusion time scaling is presented as a precursor of the fast bifurcation. The efficiency of both precursors in a currency market was illustrated by simulation of a prototype of a trading system.

q-fin.ST↗

arXiv2015

Phase liquid turbulence as novel quantum approach

In this paper we consider a nonlinear stochastic approach to the description of quantum systems. It is shown that a possibility to derive quantum properties - spectrum quantization, zero point positive energy and uncertainty relations, exists in frame of Zaslavsky phase liquid. This liquid is considered as a projection of continuous turbulent medium into a Hilbert phase space.It has isotropic minimal diffusion defined by Planck constant.Areas of probability condensation may produce clustering centers: quasi stable particles-attractors which preserve boundaries and scale-free fractal transport properties.The stability of particles has been shown in frame of the first order perturbation theory. Quantum peculiarities of considered systems have been strictly derived from markovian Fokker-Planck equation. It turned out that the positive zero point energy has volumetric properties and grows for higher time resolutions. We have shown that a quasi stable attractor may be applied as a satisfactory model of an elementary quantum system. The conditions of attractor stability are defined on the basis of Nonlinear Prigogine Theorem. Finally the integrity of classical and quantum approaches is recovered: existence of particles is derived in terms of Zaslavsky quantum fluid.

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arXiv2014

Extended Prigozhin theorem: method for universal characterization of complex system evolution

Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through power of energy, injected into system and power of energy, dissipated through internal nonlinear mechanisms. It was found out that basic phase parameter as control parameter must be delimited for two types of system - accelerator and decelerator. It was suggested to select zero state entropy on through condition of zero value for entropy production. Zero state introduces universal principle of disorder characterization. On basis of self organization theorem we have derived relations for entropy production behavior in the vicinity stationary state of system. Advantage of these relations in comparison to classical Prigozhin theorem is versatility of their application to arbitrary nonlinear systems. It was found out that extended Prigozhin theorem introduces two relations for accelerator and decelerator correspondingly, which remarks their quantitative difference. At the same time classic Prigozhin theorem makes possible description of linear decelerator only. For unstable motion it corresponds to strange attractor.

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arXiv2014

Extended foundations of stochastic prediction

The basic purpose of this work was to suggest universal quantitative description of ergodic system intermediate bifurcation and obligatory conditions of this transition. Conditions for existence of phase state and first order phase transition were introduced in terms of energy balance for system volume unit. Extended Fokker - Plank equation with time dependent diffusion factor was formulated. It turned out that for ergodic system with fixed boundary quantized energy spectrum of phase stable states exists. Obtained results may be applied for prediction of ergodic system behavior. If isolation condition is satisfied, phase spectrum quantization allows selecting proper control parameters for system stabilization. Information about current system coarsened energy allows predicting of future stochastic system behavior on the basis of extended Fokker - Plank model.

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arXiv2014

Discharge convective instability as modifier of nonlinear hydrodynamic spectrum

Discharge source is considered as modifier of flow hydrodynamic spectrum. Characteristic frequency of nonlinear spectrum and spectrum power were determined under conditions of arc sliding discharge in supersonic flow. Two stages of discharge were defined: sliding stage and still stage. It was found that stage transition occurs due to convective instability of discharge. Fraction of sliding stage in overall discharge duration is determined by averaged current that is general stable discharge parameter. This phenomenon gives opportunity to control power of pressure fluctuations spectrum. Theoretical insight of field and hydrodynamic factors influencing on pulsations frequency was achieved. Hydrodynamic resistance of discharge region and holding cathode electric field turned out to be basic factors of frequency modification. Corresponding experimental verification was taken. Basic frequency law was determined for several discharge regimes.

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arXiv2014

Extended Fokker Planck model: properties and solutions

In the current paper Fokker Planck model of random walks has been extended to non conservative cases characterized by explicit dependence of diffusion and energy on time. A given generalization allows describing of such non equilibrium processes as Levy flights in a classical differential form without use of fractal PDE. Besides it takes into account mixing properties that are obligatory for a certain class of chaotic systems such as Kolmogorov K system. It was shown that an abnormal transport is a consequence of the equilibrium distortion and not stationary diffusion. The particular case of fixed boundaries was considered. According to the received solutions it was shown that a system structure can resist a weak disturbance in the vicinity of the discrete regimes, defined by a system scale and its nonlinear properties. These regimes correspond to the exponential increase of quasi regular structure fluctuations. Only fast disruption of regime is possible for other states of the system. It leads to an immediate transition to the chaos.

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