Related papers: Fundamental theorem for quantum asset pricing
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
The main purpose of this article is to evaluate possible applications of quantum computers in foreign exchange reserves management. The capabilities of quantum computers are demonstrated by means of risk measurement using the quantum Monte…
We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with…
We reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. Two of the authors have recently proposed a quantum description of financial market in terms…
We present a version of the fundamental theorem of asset pricing (FTAP) for continuous time large financial markets with two filtrations in an $L^p$-setting for $ 1 \leq p < \infty$. This extends the results of Yuri Kabanov and Christophe…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…
We consider a Quantum Computer with n quantum-bits (`qubits'), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we suggest a quantification for the property…
We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the index is a tradable security, we also assume that it is…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…
The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which…
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes…
Motivated by Heisenberg's observable-only stance, we replace latent "information" (filtrations, hidden diffusions, state variables) with observable transitions between price states. On a discrete price lattice with a Hilbert-space…
In this paper a finite discrete time market with an arbitrary state space and bid-ask spreads is considered. The notion of an equivalent bid-ask martingale measure (EBAMM) is introduced and the fundamental theorem of asset pricing is proved…
We consider the psychological effect of preference reversal and show that it finds a natural explanation in the frame of quantum decision theory. When people choose between lotteries with non-negative payoffs, they prefer a more certain…
We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with overwhelming probability: if the density is below $1/2$, the…
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…
Several benchmarks have been proposed to holistically measure quantum computing performance. While some have focused on the end user's perspective (e.g., in application-oriented benchmarks), the real industrial value taking into account the…
Machine learning and quantum machine learning (QML) have gained significant importance, as they offer powerful tools for tackling complex computational problems across various domains. This work gives an extensive overview of QML uses in…