This paper proposes a quantum mechanical state equation for describing evolution of projects of financial investment, while the parameters of this equation well simulate the fundamental elements of financial market, including investment (input), assets loss (assets decrease), assets increase and income (output), the quantum mechanics operators involved in this equation also can reflect the dynamic process and characteristics of the project, so the equation can be taken as the evolution model of a kind of financial investment projects in the market. The entangled state representation is introduced to solve this equation and its solution is obtained in an infinite operator-sum form, which exhibits the link between the initial state and final state, i.e., the dynamic process of the financial investment project. As an example, we derive the evolution law of a pure investment project in financial market, which conforms with the evolution trend of the market. In solving the equation we also find a new state which we name it as the binomial-negative binomial entangled state. Throughout the discussions we make full use of Dirac's symbolic method and the technique of integration within an ordered product (IWOP) of operators.
This paper proposes a quantum mechanical state equation for describing evolution of projects of financial investment, while the parameters of this equation well simulate the fundamental elements of financial market, including investment (input), assets loss (assets decrease), assets increase and income (output), the quantum mechanics operators involved in this equation also can reflect the dynamic process and characteristics of the project, so the equation can be taken as the evolution model of a kind of financial investment projects in the market. The entangled state representation is introduced to solve this equation and its solution is obtained in an infinite operator-sum form, which exhibits the link between the initial state and final state, i.e., the dynamic process of the financial investment project. As an example, we derive the evolution law of a pure investment project in financial market, which conforms with the evolution trend of the market. In solving the equation we also find a new state which we name it as the binomial-negative binomial entangled state. Throughout the discussions we make full use of Dirac's symbolic method and the technique of integration within an ordered product (IWOP) of operators.
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 examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of the binomial market. Furthermore, we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering multi-period quantum binomial markets.
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 market themselves have quantum properties. In this work, we consider a financial setting where instead of by classical probabilities the market is described by a pure quantum state or, more generally, a quantum density operator. This setting naturally leads to a new asset class, which we call quantum assets. Under the assumption that such assets have a price and can be traded, we develop an extended definition of arbitrage to quantify gains without the corresponding risk. Our main result is a quantum version of the first fundamental theorem of asset pricing. If and only if there is no arbitrage, there exists a risk-free density operator under which all assets are martingales. This density operator is used for the pricing of quantum derivatives. To prove the theorem, we study the density operator version of the Radon-Nikodym measure change. We provide examples to illustrate the theory.
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 mechanics. Trajectories of prices are determined by two financial potentials: classical-like V ( q ) ("hard" market conditions, e.g., natural resources) and quantum-like U ( q ) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand, (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others).
Quantum finance is a new paradigm in financial market operations, based on the principles of quantum computing in solving highly complex problems with efficiency. This chapter covers some basic ideas of quantum finance through its historical context and the role it has played in surmounting the limitations of classical financial models. The chapter commences with the basics, including the need for an introduction to quantum mechanics, qubits, quantum gates, and algorithms that can be applied in financial applications to demonstrate how quantum computing can change finance. We discuss some of those areas where this technology is bound to make an impact: in portfolio optimization, quantum computing considers several combinations of assets at a time; in risk management, improved models will allow for better predictions of market movements; in derivative pricing, the calculations are faster and more accurate; and in fraud detection, it enables one to execute better analysis of transactional data. The advancement of quantum finance is linked to the need to resolve ethical, legal, and technical obstacles while integrating with traditional financial institutions. The financial markets will be a key source of innovation that will drive efficiency, precision, and invention to previously unheard-of heights, given the direction that quantum computing technology is expected to take. Thus, the chapter ends with a call for more study and cooperation to fully grasp quantum finance's transformative potential.
The development of quantum entanglement opens new opportunities for financial markets, facilitating faster data processing, optimizing strategies and improving risk management. Quantum algorithms, with their exponential computational power, are able to solve problems available for classical computers, which makes them promising for high-frequency trading, stress testing of banking systems and liquidity analysis. Introduction of quantum cryptography and optimization algorithms changes the approach to the security of financial operations and forecasting of asset dynamics. The article discusses the main directions of quantum computers use in finance, analyzes their consequences, potential threats and regulatory challenges. Special attention is paid to the impact of the quantum revolution on the financial sector of the economy and the possibility of its transition to new technologies.
Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a model based on the quantum walk algorithm are compared with those obtained from classical methodologies. We focus on specific limitations of the classical models, and illustrate that the quantum walk model possesses great flexibility in overcoming these. This includes the potential to generate asymmetric return distributions with complex market tendencies and higher probabilities for extreme events than in some of the classical models. Furthermore, the temporal evolution in the quantum walk possesses the potential to provide asset price dynamics.