We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the geodesic equation in the space of black hole masses. This provides a novel geometric interpretation for the decay of black holes. Moreover, this approach pred...

Financial options whose payoff depends critically on historical prices are called pathdependent options. Their prices are usually harder to calculate than options whose prices do not depend on past histories. Asian options are popular path-dependent derivatives, and it has been a long-standing problem to price them efficiently and accurately. No known exact pricing formulas are available to pri...

We study a revised version of Witten’s 2d black hole, in which the matter and (b, c) ghosts are mixed. The level of the coset model is still 9/4. We show that this model is equivalent to that of Mukhi and Vafa, in which the level of the coset model is taken as 3, and the stress tensor is improved. We argue that the exact metric in such a model is just the semi-classical one, quite different fro...

It has been, recently pointed out that the initial value problem in new inflation models is naturally solved by supergravity effects if there exists a pre-inflation before the new inflation. We study this double inflation model in details and find that density fluctuations on small cosmological scales are much larger than those on large scales due to peculiar property of the new inflation. We s...

There are many references showing that a classical solution to the Black–Scholes equation is a stochastic solution. However, it is the converse of this theorem which is most relevant in applications and the converse is also more mathematically interesting. In the present article we establish such a converse. We find a Feynman–Kac type theorem showing that the stochastic representation yields a ...

We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is ...

This paper addresses a finite difference approximation for an infinite dimensional Black-Scholes equation obtained in Chang and Youree [5]. The equation arises from a consideration of an European option pricing problem in a market in which stock prices and the riskless asset prices have hereditary structures. Under a general condition on the payoff function of the option, it is shown that the p...