Quantum Portfolios of Observables and the Risk Neutral Valuation Model

Details Quantum Portfolios of Observables and the Risk Neutral Valuation Model Quantum Portfolios of Observables and the Risk Neutral Valuation Model

2010-04-02

arxiv.org/abs/1004.0844v1

Economy

Quantitative Finance

General Finance

8 pages, no figures

Scientific paper

Quantum Portfolios of quantum algorithms encoded on qbits have recently been reported. In this paper a discussion of the continuous variables version of quantum portfolios is presented. A risk neutral valuation model for options dependent on the measured values of the observables, analogous to the traditional Black-Scholes valuation model, is obtained from the underlying stochastic equations. The quantum algorithms are here encoded on simple harmonic oscillator (SHO) states, and a Fokker-Planck equation for the Glauber P-representation is obtained as a starting point for the analysis. A discussion of the observation of the polarization of a portfolio of qbits is also obtained and the resultant Fokker-Planck equation is used to obtain the risk neutral valuation of the qbit polarization portfolio.

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