Interviewer: First I must mention that I cannot recall ever having heard of a self-interview. Would you mind saying how you came to interview yourself about your new theory? Donald Black: I decided to interview myself partly because I have never been entirely satisfied with the questions interviewers have asked me in the past (see, e.g., Black, 2002a; 2010b). I thought I might be able to ask be...

We investigate when a hedger who over-estimates the volatility will superreplicate a convex claim on several underlying assets. It is shown that the classical Black and Scholes model is the only model, within a large class, for which over-estimation of the volatility yields the desired superreplication property. This is in contrast to the onedimensional case, in which it is known that over-esti...

References [1] F. Black and P. Karasinski, Bond and option pricing when short-term rates are lognormal, Financial Analysts Journal, Vol. 47, No. 4, 52-59, 1991. [2] F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy, Vol. 81, 637-654, 1973. [3] J. C. Cox, J. E. Ingersoll, and S.A. Ross, An intertemporal general equilibrium model of asset pric...

ii Acknowledgments I am grateful to my supervisor, Wulin Suo, for giving me the opportunity to evaluate the empirical performance of the Black-Scholes Model and the GARCH option pricing model and for his exceptional comments on my manuscript. Also, I dedicate this paper to my family and my love, who always supported and encouraged me in the writing process.

Black and Scholes (1973) proved that under certain assumptions about the market place, the value of a European option, as a function of the current value of the underlying asset and time, verifies a Cauchy problem. We give new conditions for the existence and uniqueness of the value of a European option by using semigroup theory. For this, we choose a suitable space that verifies some condition...

We consider two families of D1-D5-P states and find their gravity duals. In each case the geometries are found to ‘cap off’ smoothly near r = 0; thus there are no horizons or closed timelike curves. These constructions support the general conjecture that the interior of black holes is nontrivial all the way up to the horizon.

Christian M Jones Laura Scholes Daniel Johnson Mary Katsikitis Michelle C. Carras University of the Sunshine Coast University of the Sunshine Coast Queensland University of Technology University of the Sunshine Coast Johns Hopkins University Queensland, Australia Queensland, Australia Queensland, Australia Queensland, Australia Baltimore, MD, USA [email protected] [email protected] dm.johns...

A Dissertation submitted for the Degree of Doctor of Philosophy To the memory of my mother Contents Preface iii 1 Introduction 1 1.1 Option pricing in discrete time 1 1.2 Option pricing in continuous time 4 1.3 The Black-Scholes model 8 1.4 Interest-rate models 9

Following a short account of the history of the idea of black holes, we present a review of the current status of the search for observational evidence of their existence aimed at an audience of relativists rather than astronomers or astrophysicists. We focus on two different regimes: that of stellar-mass black holes and that of black holes with the masses of galactic nuclei.