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Interest Rates and Information Geometry
Dorje C. Brody, Lane P. Hughston
The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distrib…
General Theory of Geometric Lévy Models for Dynamic Asset Pricing
Dorje C. Brody, Lane P. Hughston, Ewan Mackie
The geometric Lévy model (GLM) is a natural generalisation of the geometric Brownian motion model (GBM) used in the derivation of the Black-Scholes formula. The theory of such mode…
Theory of Information Pricing
Dorje C. Brody, Yan Tai Law
In financial markets valuable information is rarely circulated homogeneously, because of time required for information to spread. However, advances in communication technology mean…
Coquaternionic quantum dynamics for two-level systems
Dorje C. Brody, Eva-Maria Graefe
The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristic…
Six-dimensional space-time from quaternionic quantum mechanics
Dorje C. Brody, Eva-Maria Graefe
Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle…
Noise, risk premium, and bubble
Grzegorz Andruszkiewicz, Dorje C. Brody
The existence of the pricing kernel is shown to imply the existence of an ambient information process that generates market filtration. This information process consists of a signa…