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Home  >  Volume 38

3. On the Quantum Binomial Models with Stochastic Differential Equation Satisfying the Law of Iterated Logarithm Bright O. Osu and Philip U. Uzoma Volume 38, (November, 2016), pp 13 – 22
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This study aims at connecting quantum binomial model with stochastic differential equation satisfying the law of iterated logarithm and its application to pricing contingent claims in modern finance. It is first shown that the process X(t)  called Brownian motion on the unit circle satisfies a linear stochastic differential equation (SDE) which obeys the law of iterated logarithm (LIL). Then given two such processes, X_1 (t), and X_2 (t), say, another linear SDE is constructed in matrix form. It is observed that the coefficient K ofX(t) of this new SDE is the same as the Heisenberg’s generated matrices modelled by self-adjoint Hilbert space operators. These matrices are further applied to the single period quantum binomial model to show arbitrage freedom (given some conditions), when an observer measures the stock market.

Key words: Quantum binomial model, linear stochastic differential equation, Heisenberg’s matrices, Law of iterated logarithm, stock market.