37 research outputs found
The Quantum Black-Scholes Equation
Motivated by the work of Segal and Segal on the Black-Scholes pricing formula
in the quantum context, we study a quantum extension of the Black-Scholes
equation within the context of Hudson-Parthasarathy quantum stochastic
calculus. Our model includes stock markets described by quantum Brownian motion
and Poisson process.Comment: Has appeared in GJPAM, vol. 2, no. 2, pp. 155-170 (2006
Spectral Theorem Approach to the Characteristic Function of Quantum Observables
We compute the resolvent of the anti-commutator operator and of the
quantum harmonic oscillator Hamiltonian operator . Using
Stone's formula for finding the spectral resolution of an, either bounded or
unbounded, self-adjoint operator on a Hilbert space, we also compute their
Vacuum Characteristic Function (Quantum Fourier Transform). We also show how
Stone's formula is applied to the computation of the Vacuum Characteristic
Function of finite dimensional quantum observables. The method is proposed as
an analytical alternative to the algebraic (or Heisenberg) approach relying on
the associated Lie algebra commutation relations
Von Neumann\u27s Minimax Theorem for Continuous Quantum Games
The concept of a classical player, corresponding to a classical random
variable, is extended to include quantum random variables in the form of self
adjoint operators on infinite dimensional Hilbert space. A quantum version of
Von Neumann's Minimax theorem for infinite dimensional (or continuous) games is
proved