Finite state Markov chains and prediction of stock market trends using real data

In this thesis we discuss finite state Markov chains, which are a special class of stochastic processes. They can be represented either by a graph or by a matrix [P]. The reader is first introduced to Markov chains and is then guided in their classification. Some relevant theorems are discussed. The results are used to explain when [P^n], the matrix obtained by taking the nth power of [P], converges as n approaches infinity. We start by studying the convergence in the case of [P] > 0 and we continue by focusing on two specific kinds of Markov chains: ergodic finite state chains and ergodic unichains. We then cover more general types of chains. In the end we give an example of how these tools can be used in the field of finance. We develop a model that predicts fluctuations in the prices of stocks and we apply it to the FTSE-MIB Index using data from Borsa Italiana

Efficient Electrochemical Reduction of CO2 to Formate in Methanol Solutions by Mn Functionalized Electrodes in the Presence of Amines

Carbon cloth electrode modified by covalently attaching a manganese organometallic catalyst is used as cathode for the electrochemical recuction of CO2 in methanol solutions. Six different amines are employed as co-catalyst in millimolar concentrations, which coupled to the increased solubility of CO2 in methanol enhance the formate production, switch the selectivity toward formate anion, and in the case of pentamethyldiethylentriamine (PMDETA) resulted in an impressive TONHCOO– of 2.8×104. We demonstrate that the protonated PMDETA is formed in methanol solution by simply bubbling CO2, which is the responsible for a barrierless transformation of CO2 to formate via the reduced form of the Mn catalyst covalently bonded to the electrode surface. These findings pave the way for more efficient transformation of CO2 into liquid fuel and shed light on the electrochemical mechanis