A probabilistic approach for financial IoT data

The extraction of information from the Internet of Things (IoT) plays a fundamental role in many research fields. In this work we focus our attention on financial data, used to describe self-financing portfolios in a complete market. Here, the absence of the arbitrage principle, the existence and the uniqueness of no arbitrage price are valid. With these hypotheses we can resort to the Black-Scholes model in order to determine the expression of no arbitrage price. In this model, frictional costs are avoided. Moreover, selling and buying of every amount of the assets and short sellings are allowed. In other words, traders can sell amount of assets even if they do not own them. Finally, this model is composed by a risk-free and a Geometric Brownian motion risk assets.