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Kirill Ilinski

Publications and source records attributed to Kirill Ilinski.

12 recordsLinked to original sources
arXiv2004

New Application of Functional Integrals to Classical Mechanics

In this paper a new functional integral representation for classical dynamics is introduced. It is achieved by rewriting the Liouville picture in terms of bosonic creation-annihilation operators and utilizing the standard derivation of functional integrals for dynamical quantities in the coherent states representation. This results in a new class of functional integrals which are exactly solvable and can be found explicitly when the underlying classical systems are integrable.

cond-mat.stat-mech↗
arXiv1999

Critical Crashes?

In this short note we discuss recent attempts to describe pre-crash market dynamics with analogies from theory of critical phenomena.

cond-mat.stat-mech↗
arXiv1999

How to reconcile Market Efficiency and Technical Analysis

Weak form of the Efficiency Market Hypothesis (EMH) excludes predictions of future market movements from historical data and makes the technical analysis (TA) out of law. However the technical analysis is widely used by traders and speculators who steadely refuse to consider the market as a "fair game" and survive with such believe. In the paper we make a conjecture that TA and EMH correspond to different time regimes and show how both technical analysis predictions for short times and realistic statistical data for larger times can be obtained in a simple single stock model of Gauge Theory of Arbitrage.

cond-mat.stat-mech↗
arXiv1999

Virtual Arbitrage Pricing Theory

We generalize the Arbitrage Pricing Theory (APT) to include the contribution of virtual arbitrage opportunities. We model the arbitrage return by a stochastic process. The latter is incorporated in the APT framework to calculate the correction to the APT due to the virtual arbitrage opportunities. The resulting relations reduce to the APT for an infinitely fast market reaction or in the case where the virtual arbitrage is absent. Corrections to the Capital Asset Pricing Model (CAPM) are also derived.

cond-mat.stat-mech↗
arXiv1999

Derivative pricing with virtual arbitrage

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equation which, in the absence of the virtual arbitrage or for an infinitely fast market reaction, reduces to the Black-Scholes equation. Explicit formulas are obtained for European call and put vanilla options.

cond-mat.stat-mech↗
arXiv1998

Black-Scholes equation from Gauge Theory of Arbitrage

We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and speculators reaction on it. The model accounts for both violation of the no-arbitrage constraint and non-Brownian price walks which resemble real financial data. The correction is nonlocal and transform the differential Black-Scholes equation to an integro-differential one.

hep-th↗
arXiv1998

New bosonization scheme for spin systems in any dimension

We present a new representation of spin operators in terms of bosonic creation-annihilation operators. This representation allows us to formulate a new field-theoretical description of spin systems which is free of any constraints. The corresponding functional integral representations for thermodynamic quantities are given and the application to investigations of Long Range Order in the system is discussed.

cond-mat.stat-mech↗
arXiv1997

Physics of Finance

We give a brief introduction to the Gauge Theory of Arbitrage. Treating a calculation of Net Present Values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. This allows us to map the theory of capital market onto the theory of quantized gauge field interacted with a money flow field. The gauge transformations of the matter field correspond to a dilatation of security units which effect is eliminated by a gauge transformation of the connection. The curvature tensor for the connection consists of the excess returns to the risk-free interest rate for the local arbitrage operation. Free quantum gauge theory is equivalent to the assumption about the log-normal walks of assets prices. In general case the consideration maps the capital market onto lattice QED.

hep-th↗
arXiv1996

New index formulas as a meromorphic generalization of the Chern-Gauss-Bonnet theorem

Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the study of spectral properties of the operators. Analytical expressions are provided by the Heat Kernel approach in terms of the functional integrals. As a result two formulae connecting characteristics of meromorphic (real meromorphic) functions and topological properties of Riemann (separated type Klein) surfaces are derived.

hep-th↗
arXiv1996

Aspect ratio analysis for ground states of bosons in anisotropic traps

Characteristics of the initial condensate in the recent experiment on Bose-Einstein condensation (BEC) of ${}^{87}$Rb atoms in an anisotropic magnetic trap is discussed. Given the aspect ratio $R$, the quality of BEC is estimated. A simple analytical Ansatz for the initial condensate wave function is proposed as a function of the aspect ratio which, in contrast to the Baym-Pethick trial wave function, reproduces both the weak and the strong intaraction limits and which is in better agreement with numerical results than the latter.

cond-mat↗