Related papers: Fisher information and quantum mechanical models f…
We consider asymptotics of the velocity derivatives probability distribution functions (PDFs) in Burgers' turbulence. We argue that in the forced case the same power laws as in the decaying case are realized for an infinite system.
The Fisher-Bingham distribution ($\mathrm{FB}_8$) is an eight-parameter family of probability density functions (PDF) on $S^2$ that, under certain conditions, reduce to spherical analogues of bivariate normal PDFs. Due to difficulties in…
We present a financial market model, characterized by self-organized criticality, that is able to generate endogenously a realistic price dynamics and to reproduce well-known stylized facts. We consider a community of heterogeneous traders,…
In previous papers we have shown how Schrodinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The…
The quantum Fisher information matrix is a central object in multiparameter quantum estimation theory. It is usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of the…
We study the pricing of credit derivatives with asymmetric information. The managers have complete information on the value process of the firm and on the default threshold, while the investors on the market have only partial observations,…
The applications of techniques from statistical (and classical) mechanics to model interesting problems in economics and finance has produced valuable results. The principal movement which has steered this research direction is known under…
We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the…
The paper treats the financial market as a communication system, using four information-theoretic assumptions to derive an idealized model with only one parameter. State variables are scalar stationary diffusions. The model minimizes the…
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters - both their errors and covariances. In this short review, I outline a…
A new framework for asset pricing based on modelling the information available to market participants is presented. Each asset is characterised by the cash flows it generates. Each cash flow is expressed as a function of one or more…
Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this paper, we focus on derivative pricing based on solving the Black-Scholes partial…
We develop the information geometry of L\'evy processes. Deriving $\alpha$-divergences directly in terms of the L\'evy triplets of the L\'evy processes, we identify Fisher information matrix and $\alpha$-connection on the statistical…
We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…
This paper studies the asymptotic behavior of the Fisher information for a Levy process discretely sampled at an increasing frequency. We show that it is possible to distinguish not only the continuous part of the process from its jumps…
We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate…
We provide a new expression of the quantum Fisher information(QFI) for a general system. Utilizing this expression, the QFI for a non-full rank density matrix is only determined by its support. This expression can bring convenience for a…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…