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.

in this paper we consider the european continuous installment call option. then  its linear complementarity formulation is given. writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. finally finite element method is applied to price the european continuous installment call option.

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...

In [1], Borodin et al figured out a gap of [5], and gave a new proof with the similar technique. The purpose of this note is to fix the gap of [5] by slightly revising the definition of special faces, and adding a few lines of explanation in the proofs (new added text are all in black font).

We generalize the classical binomial approach of the model of Black and Scholes to a Markov binomial approach. This leads to a new formula for the cost of an option.