In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using...

Black holes are a continuing source of mystery. Although their classical properties have been understood since the 1970’s, their quantum properties raise some of the deepest questions in theoretical physics. Some of these questions have recently been answered using string theory. I will review these fundamental questions, and the aspects of string theory needed to answer them. I will then expla...

Scalar field collapse in three-dimensions. Abstract We study an analytical solution to the Einstein's equations in 2 + 1-dimensions, representing the collapse of a circularly symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters , this solution exhibits all three, known, end states of a collapse situation: Minkowski space-time after a bouncing, naked...

We study a discrete time hedging and pricing problem in a market with liquidity costs. Using Leland’s discrete time replication scheme [Leland, H.E., 1985. Journal of Finance, 1283–1301], we consider a discrete time version of the Black–Scholes model and a delta hedging strategy. We derive a partial differential equation for the option price in the presence of liquidity costs and develop a modi...

The purpose of this paper is to present a survey of recent developments concerning the distributions of occupation times of Brownian motion and their applications in mathematical finance. The main result is a closed form version for Akahori’s generalized arc-sine law which can be exploited for pricing some innovative types of options in the Black & Scholes model. Moreover a straightforward proo...

The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g., negative specific heat (not allowed in the canonical ensemble) and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses o...

This work presents a theoretical analysis for the Black–Scholes equation. Given a terminal condition, the analytical solution of the Black–Scholes equation is obtained by using the Adomian approximate decomposition technique. The mathematical technique employed in this work also has significance in studying some other problems in finance theory.

We study thermodynamic state-space geometry of the black holes in string theory and M -theory. For a large number of microstates, we analyze the intrinsic state-space geometry for (i) extremal and non-extremal black branes in string theory, (ii) multi-centered black brane configurations, (iv) small black holes with fractional branes, and (v) fuzzy rings in the setup of Mathur’s fuzzballs and su...

In this article, the authors examine the conceptualisation of Psychology of Black Identity as a multidimensional and a dynamic construct that develops over time through a process of exploration and commitment. The design of the current paper was a conceptual work based on reviewed literature ranging from the early 1930s to present (2010). The authors review research on Psychology of Black Ident...

We establish the existence of hairy black holes in su(N) Einstein-Yang-Mills theories, described by one discrete and N − 2 continuous parameters.