We have found, at least from the practical point of view, the complete solution of the option pricing problem for underlying securities obeying stochastic volatility price dynamics. Although partial solutions have existed, and in spite of a considerable attention to it, this problem has been open for about 20 years. The pricing problem is reduced to solving an uncoupled system of a Monge–Ampère...

Static spherically symmetric solutions for conformal gravity in three dimensions are found. Black holes and wormholes are included within this class. Asymptotically the black holes are spacetimes of arbitrary constant curvature, and they are conformally related to the matching of different solutions of constant curvature by means of an improper conformal transformation. The wormholes can be con...

We discuss a previous attempt at a microscopic counting of the entropy of asymptot-ically flat non-extremal black-holes. This method used string dualities to relate 4 and 5 dimensional black holes to the BTZ black hole. We show how the dualities can be justified in a certain limit, equivalent to a near horizon limit, but the resulting spacetime is no longer asymptotically flat.

We show that black holes grow substantially by accretion at close to Eddington rates. Using a complete sample of soft X-ray selected AGNs, Grupe & Mathur (2004) have shown that narrow line Seyfert 1 galaxies, as a class, lie below the MBH–σ relation of normal galaxies. Some NLS1s, however, lie on or close to the MBH–σ relation. Here we show that not all NLS1s accrete at close to Eddington rates...