An adjusted Black-Scholes pricing formula is derived in this paper. By separating risk and uncertainty through the robust control technique, we find that uncertainty as well as risk raises the management’s subjective evaluation of real options. We suggest a simple method to filter the risk of the project and to acquire a more reliable value of real options without the influence of uncertainty. ...

We prove a Donsker type approximation theorem for the fractional Brownian motion in the case H > 1/2. Using this approximation we construct an elementary market model that converges weakly to the fractional analogue of the Black–Scholes model. We show that there exist arbitrage opportunities in this model. One such opportunity is constructed explicitly.

This article studies the pricing of options in an extended Black Scholes economy in which the underlying asset is not perfectly liquid. The resulting liquidity risk is modeled as a stochastic supply curve, with the transaction price being a function of the trade size. Consistent with the market microstructure literature, the supply curve is upward sloping with purchases executed at higher price...

A string theory description of near extremal black rings is proposed. The entropy is computed and the thermodynamic properties are derived for a large family of black rings that have not yet been constructed in supergravity. It is also argued that the most general black ring in N = 8 supergravity has 21 parameters up to duality.

We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments are uncorrelated (but not necessarily independent) and of arbitrary probability density. We discuss in particular how, in the Gaussian limit, the Black-Schole...

We study how the charges of the black rings measured at the asymptotic infinity are encoded in the near-horizon metric and gauge potentials, independent of the detailed structure of the connecting region. Our analysis clarifies how different sets of four-dimensional charges can be assigned to a single five-dimensional object under the Kaluza-Klein reduction. Possible choices are related by the ...

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...