Related papers: Fisher information and quantum mechanical models f…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be…
The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
The paper deals with the reformulation of quantum uncertainty relation involving position and momentum of a particle on the basis of the Kerridge measure of inaccuracy and the Fisher information.
In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…
In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As…
We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of…
Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding…
The Bohmian quantum approach is implemented to analyze the financial markets. In this approach, there is a wave function that leads to a quantum potential. This potential can explain the relevance and entanglements of the agent's behaviors…
The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…
For a given metric $g_{\mu\nu}$, which is identified as Fisher information metric, we generate new constraints for the probability distributions for physical systems. We postulate the existence of intrinsic probability distributions for…
Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both…
We derive explicit expressions for the quantum Fisher information and the symmetric logarithmic derivative (SLD) of a quantum state in the exponential form; the SLD is expressed in terms of the generator. Applications include…
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
Csiszar's f-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting positive semidefinite matrices are in the place of probability distributions and the quantum…
A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as…
In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given…