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This paper presents a new approach to interest rate dynamics. We consider the general family of arbitrage-free positive interest rate models, valid on all time horizons, in the case of a discount bond system driven by a Brownian motion of one or more dimensions. We show that the space of such models admits a canonical mapping to the space of… (More)

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)

- Dorje C. Brody, Lane P. Hughston, Andrea Macrina
- 2006

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)

A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the space of all square-integrable functions. More precisely, by consideration of the square-root… (More)

An asymmetric information model is introduced for the situation in which there is a small agent who is more susceptible to the flow of information in the market than the general market participant, and who tries to implement strategies based on the additional information. In this model market participants have access to a stream of noisy information… (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)

- Edward Hoyle, Lane P. Hughston, Andrea Macrina
- 2010

We develop a non-life reserving model using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an arbitrary choice of a priori distribution for the ultimate loss. Taking a Bayesian approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The 'best-estimate ultimate loss… (More)

- Dorje C. Brody, Lane P. Hughston, Andrea Macrina
- 2010

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)

- Dorje C. Brody, Irene C. Constantinou, James D. C. Dear, Lane P. Hughston
- 2008

A closed-form solution to the energy-based stochastic Schrödinger equation with a time-dependent coupling is obtained. The solution is algebraic in character, and is expressed directly in terms of independent random data. The data consist of (i) a random variable H which has the distribution P(H = E i) = π i , where π i is the transition probability |ψ 0 |φ… (More)

- Lane P. Hughston
- 2008

A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski space is proposed and its properties examined. In this scheme the structure of space-time is intrinsically quantum… (More)