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10: Paper Source PDF document

Paper's Title:

Bartle Integration in Lie Algebras


Andreas Boukas and Philip Feinsilver

Centro Vito Volterra,
Universita di Roma Tor Vergata,
via Columbia 2, 00133 Roma,

Department of Mathematics,
Southern Illinois University,
Carbondale, Illinois 62901,



Using Bartle's bilinear vector integral we define stochastic integrals of bounded operator valued functions with respect to Stieltjes measures associated with the generators of the Heisenberg and Finite Difference Lie algebras. Our definition also covers the Square of White Noise and sl/2 Lie algebras.

6: Paper Source PDF document

Paper's Title:

On the Fock Representation of the Central Extensions of the Heisenberg Algebra


L. Accardi and A. Boukas

Centro Vito Volterra, UniversitÓ di Roma Tor Vergata,
via Columbia 2, 00133 Roma,

Department of Mathematics,
American College of Greece,
Aghia Paraskevi, Athens 15342,


We examine the possibility of a direct Fock representation of the recently obtained non-trivial central extensions of the Heisenberg algebra, generated by elements and E satisfying the commutation relations ,  and , where a and are dual, h is self-adjoint, E is the non-zero self-adjoint central element and We define the exponential vectors associated with the Fock space, we compute their Leibniz function (inner product), we describe the action of a, and h on the exponential vectors and we compute the moment generating and characteristic functions of the classical random variable corresponding to the self-adjoint operator

3: Paper Source PDF document

Paper's Title:

On Segal's Quantum Option Pricing


Andreas Boukas

Department of Mathematics and Natural Sciences,
American College of Greece
Aghia Paraskevi 15342, Athens,


We apply the non-commutative extension of classical It˘ stochastic calculus, known as quantum stochastic calculus, to the quantum Black-Scholes model in the sense of Segal and Segal [4]. Explicit expressions for the best quantum option price and the associated optimal quantum portfolio are derived.

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