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The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for…
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for…
Existing approaches to asset-pricing under model-uncertainty adapt classical utility-maximization frameworks and seek theoretical comprehensiveness. We move toward practice by considering binary model-risks and by emphasizing 'constraints'…
Quantum theory provides a comprehensive framework for quantifying uncertainty, often applied in quantum finance to explore the stochastic nature of asset returns. This perspective likens returns to microscopic particle motion, governed by…
In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model…
We propose a new idea for public key quantum money. In the abstract sense, our bills are encoded as a joint eigenstate of a fixed system of commuting unitary operators. We perform some basic analysis of this black box system and show that…
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation…
The relationship between expectation and price is commonly established with two principles: no-arbitrage, which asserts that both maps are positive; and equivalence, which asserts that the maps share the same null events. Constructed from…
Financial models based on the Wick product, and White Noise formalism have previously been suggested in order to incorporate integrals with respect to fractional Brownian motion. It has also been pointed out that this leads naturally to a…
The financial sector is anticipated to be one of the first industries to benefit from the increased computational power of quantum computers, in areas such as portfolio optimisation and risk management to financial derivative pricing.…
This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability…
We study asset price bubbles in market models with proportional transaction costs $\lambda\in (0,1)$ and finite time horizon $T$ in the setting of [49]. By following [28], we define the fundamental value $F$ of a risky asset $S$ as the…
We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real…
We continue the analysis of quantum-like description of market phenomena and economics. We show that it is possible to define a risk inclination operator acting in some Hilbert space that has a lot of common with quantum description of the…
A digital currency is money in a digital form. In this model, maintaining integrity of the supply is a core concern, therefore protections against double-spending are often at the heart of a secure digital money scheme. Quantum money…
Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key, meaning…
A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is…
In finance, assessing the creditworthiness of loan applicants requires lenders to cluster borrowers using rating scales. Financial institutions must define the scales in compliance with strict institutional constraints, resulting in solving…