相关论文: Information and Arbitrage: Applications of Quantum…

Quantum computers have the potential to provide an advantage for financial pricing problems by the use of quantum estimation. In a broader context, it is reasonable to ask about situations where the market and the assets traded on the…

Option pricing is the most elemental challenge of mathematical finance. Knowledge of the prices of options at every strike is equivalent to knowing the entire pricing distribution for a security, as derivatives contingent on the security…

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…

This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that…

We explore nature of price formation in financial markets and develop a theory of bid and ask price dynamics in which the two prices form due to quantum-chaotic interaction between buy and sell orders. In this model bid and ask prices are…

Drawing on set theory, this paper contributes to a deeper understanding of the structural condition of mathematical finance under Knightian uncertainty. We adopt a projective framework in which all components of the model -- prices, priors…

The algebra of transactions as fundamental measurements is constructed on the basis of the analysis of their properties and represents an expansion of the Boolean algebra. The notion of the generalized economic measurements of the economic…

We reconsider the microeconomic foundations of financial economics. Motivated by the importance of Knightian Uncertainty in markets, we present a model that does not carry any probabilistic structure ex ante, yet is based on a common order.…

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…

The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S&P 500. Persistent differences between the two prices…

We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly…

Modern approaches to stock pricing in quantitative finance are typically founded on the 'Black-Scholes model' and the underlying 'random walk hypothesis'. Empirical data indicate that this hypothesis works well in stable situations but, in…

The Group Quantization formalism is a scheme for constructing a functional space that is an irreducible infinite dimensional representation of the Lie algebra belonging to a dynamical symmetry group. We apply this formalism to the…

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…

In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of ${\bf R}^3,$ whose radius is a function of the risk-free…

The 'expected utility hypothesis' and 'Savage's Sure-Thing Principle' are violated in real life decisions, as shown by the 'Allais' and 'Ellsberg paradoxes'. The popular explanation in terms of 'ambiguity aversion' is not completely…

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…

Econophysics has developed as a research field that applies the formalism of Statistical Mechanics and Quantum Mechanics to address Economics and Finance problems. The branch of Econophysics that applies of Quantum Theory to Economics and…

This paper presents the contemporary Fundamental Theorem of Asset Pricing as being equivalent to approaches to pricing that emerged before 1700 in the context of Virtue Ethics. This is done by considering the history of science and…

Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes…