This research examines whether stock prices in the Indian markets follow a Geometric Brownian Motion (GBM). study is keen on knowing if one can predict simulated accurately against actual prices. One-year, three-year, and five-year data of historical 50 stocks listed S&P BSE (Bombay Stock Exchange) Sensex Index were employed as base to using Monte Carlo simulation's GBM method. investigates...

Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by nonergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average. A common tactic for bringing time averages closer to ensemble averages is diversifi...

In this paper we provide a real (investment) options ́ valuation method with controls that capture managerial intervention and learning (exploration, R&D, advertising, marketing research, etc.). In contrast to the standard wait-and-see approach of the real options literature, we assume that managers possess the ability to intervene either for value enhancement, or for information acquisition, an...

The geometric Brownian motion (GBM) process is frequently invoked as a model for such diverse quantities as stock prices, natural resource prices, and the growth in demand for products or services. We discuss a process for checking whether a given time series follows the GBM process. Methods to remove seasonal variation from such a time series are also analyzed. Of four industries studied, the ...

We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends the results proved in [4] in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection with the c...

In this paper, we continue the study of the geometry of Brownian motions which are encoded by Kolmogorov-Chaitin random reals (complex oscillations). We unfold Kolmogorov-Chaitin complexity in the context of Brownian motion and specifically to phenomena emerging from the random geometric patterns generated by a Brownian motion.

This paper extends the marketed asset disclaimer approach for real option valuation. In sharp contrast to the dominant real option valuation that assumes a stochastic process for an investment’s capital value, this paper demonstrates the valuation of a real option assuming that cash flow follows a stochastic process. We show that this method is at least equally effective and sometimes more intu...