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...

The option pricing problem is one of central contents in modern finance. In this paper, European option pricing formula is formulated for fuzzy financial market and some mathematical properties of them are discussed. This formula may be regarded as the fuzzy counterpart of Black-Scholes option pricing formula. In addition, some illustrative examples are also documented with MATLAB codes. c ©200...

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

In [3] it was shown that by writing the solution of the Black-Scholes partial differential equation on a small set of basis functions the computing time can be dramatically reduced. In this study we explore the generalization of the technique to basket options.