Quantum Finance
By M. Schaden. 2002
228 citations recorded by the source corpus.
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 securities and cash is taken as the basis of the Hilbert space of market states. The temporal evolution of an isolated market is unitary in this space. Linear operators representing basic financial transactions such as cash transfer and the buying or selling of securities are constructed and simple model Hamiltonians that generate the temporal evolution due to cash flows and the trading of securities are proposed. The Hamiltonian describing financial transactions becomes local when the profit/loss from trading is small compared to the turnover. This approximation may describe a highly liquid and efficient stock market. The lognormal probability distribution for the price of a stock with a variance that is proportional to the elapsed time is reproduced for an equilibrium market. The asymptotic volatility of a stock in this case is related to the long-term probability that it is traded.
Subfields: Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/30c129b59713a38f6c74a6260a7b3d9ed3fc7a75
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Economics and Econometrics
In Finance
Citations in the corpus
- Quantum Structure in Cognition (2008, methodology): “…in approaches where quantum aspects are similarly used in the modeling of these effects (Busemeyer, Matthew & Wang, 2006; Franco, 2007; Khrennikov, 2008), and that also in economics quantum mechanics has been used for modeling purposes (Schaden, 2002; Baaquie, 2004; Haven, 2005; Khrennikov, 2009).”