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Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a systematic use of the methods of martingale theory. An analysis is carried out to determine the magnitude of the fluctuations… (More)

The geometric Lévy model (GLM) is a natural generalization of the geometric Brownian motion (GBM) model used in the derivation of the Black–Scholes formula. The theory of such models simplifies considerably if one takes a pricing kernel approach. In one dimension, once the underlying Lévy process has been specified, the GLM has four parameters: the initial… (More)

Associated with every positive interest term structure there is a probability density function over the positive half line. This fact can be used to turn the problem of term structure analysis into a problem in the comparison of probability distributions, an area well developed in statistics, known as information geometry. The information-theoretic and… (More)

We consider a financial contract that delivers a single cash flow given by the terminal value of a cumulative gains process. The problem of modelling such an asset and associated derivatives is important, for example, in the determination of optimal insurance claims reserve policies, and in the pricing of reinsurance contracts. In the insurance setting,… (More)

In this paper, we will show that a vanishing generalized concurrence of a separable state can be seen as an algebraic variety called the Segre variety. This variety define a quadric space which gives a geometric picture of separable states. For pure, biand three-partite states the variety equals the generalized concurrence. Moreover, we generalize the Segre… (More)

- L. P. Hughston, W. T. Shaw
- IMA Conference on the Mathematics of Surfaces
- 1988

- Paweł Nurowski, L. P. Hughston, David Robinson
- 1998

The geometry ofP , the bundle of null directions over an Einstein spacetime, is studied. The full set of invariants of the naturalG-structure on P is constructed using the Cartan method of equivalence. This leads to an extension of P which is an elliptic fibration over the spacetime. Examples are given which show that such an extension, although natural, is… (More)

We consider the problem of optimally stopping a general one-dimensional Itô diffusion X. In particular, we solve the problem that aims at maximising the performance criterion Ex [exp(− ∫ τ 0 r(Xs) ds)f (Xτ )] over all stopping times τ , where the reward function f can take only a finite number of values and has a ‘staircase’ form. This problem is partly… (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)

We examine the geometry of the state space of a relativistic quantum field. The mathematical tools used involve complex algebraic geometry and Hilbert space theory. We consider the Kähler geometry of the state space of any quantum field theory based on a linear classical field equation. The state space is viewed as an infinite dimensional complex projective… (More)