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.

An option is a nancial contract whose value depends on that of an underlying asset such as a company stock. The Black-Scholes model for option pricing, published in 1973, revolutionized the nancial industry by introducing a no-arbitrage paradigm for valuing uncertainty and hedging against risk. This simple model assumes that the underlying stock price follows a stochastic Brownian motion proces...

In 1966, Claude Berge proposed the following sorting problem. Given a string of n alternating white and black pegs, rearrange the pegs into a string consisting of ⌈n 2 ⌉ white pegs followed immediately by ⌊n 2 ⌋ black pegs (or vice versa) using only moves which take 2 adjacent pegs to 2 vacant adjacent holes. Berge’s original question was generalized by considering the same sorting problem usin...

I criticise the view that the relativity and equivalence principles are consequences of the small-scale structure of the metric in general relativity, by arguing that these principles also apply to systems with non-trivial self-gravitation and hence non-trivial spacetime curvature (such as black holes). I provide an alternative account, incorporating aspects of the criticised view, which allows...

The authors recently discovered some interesting relations between the Black-Scholes formula and last passage times of the Brownian exponential martingales, which invites one to seek analogous results for last passage times up to a …nite horizon. This is achieved in the present paper, where Yuri’s formula, as originally presented in Akahori, Imamura and Yano (2008), is also derived. We are most...