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The manifold of pure quantum states can be regarded as a complex projective space endowed with the unitary-invariant Riemannian geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given quantum system can be represented by specific geometrical features that are selected and(More)
A new approach to credit risk modelling is introduced that avoids the use of inaccessible stopping times. Default events are associated directly with the failure of obligors to make contractually agreed payments. Noisy information about impending cash flows is available to market participants. In this framework the market filtration is modelled explicitly,(More)
We examine the geometry of the state space of a relativistic quantum eld. The mathematical tools used involve complex algebraic geometry and Hilbert space theory. We consider the KK ahler geometry of the state space of any quantum eld theory based on a linear classical eld equation. The state space is viewed as an innnite dimensional complex projective(More)
This paper presents an overview of information-based asset pricing. In the information-based approach, an asset is defined by its cash-flow structure. The market is assumed to have access to " partial " information about future cash flows. Each cash flow is determined by a collection of independent market factors called X-factors. The market filtration is(More)
Lévy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Lévy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the(More)