25 research outputs found
Pseudo Hermitian formulation of Black-Scholes equation
We show that the non Hermitian Black-Scholes Hamiltonian and its various
generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly
constructed for this class of Hamitonians. It is also shown that the effective
Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system
Risk, ambiguity and quantum decision theory
In the present article we use the quantum formalism to describe the effects
of risk and ambiguity in decision theory. The main idea is that the
probabilities in the classic theory of expected utility are estimated
probabilities, and thus do not follow the classic laws of probability theory.
In particular, we show that it is possible to use consistently the classic
expected utility formula, where the probability associated to the events are
computed with the equation of quantum interference. Thus we show that the
correct utility of a lottery can be simply computed by adding to the classic
expected utility a new corrective term, the uncertainty utility, directly
connected with the quantum interference term.Comment: 1 figur
An operatorial approach to stock markets
We propose and discuss some toy models of stock markets using the same
operatorial approach adopted in quantum mechanics. Our models are suggested by
the discrete nature of the number of shares and of the cash which are exchanged
in a real market, and by the existence of conserved quantities, like the total
number of shares or some linear combination of cash and shares. The same
framework as the one used in the description of a gas of interacting bosons is
adopted
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"Potentialities or Possibilities": Towards Quantum Information Science?
The use of quantum concepts and formalisms in the information sciences is assessed through an analysis of published literature. Five categories are identified: use of loose analogies and metaphors between concepts in quantum physics and library/information science; use of quantum concepts and formalisms in information retrieval; use of quantum concepts and formalisms in studying meaning and concepts; quantum social science, in areas adjacent to information science; and the qualitative application of quantum concepts in the information disciplines. Quantum issues have led to demonstrable progress in information retrieval and semantic modelling, with less clear-cut progress elsewhere. Whether there may be a future “quantum turn” in the information sciences is debated, the implications of such a turn are considered, and a research agenda outlined