Lévy Jump-Diffusions, Market Models, and Applications

In this book, we constructed the exponential semimartingales, martingales, discrete and continuous-time stochastic processes, Lévy processes, jump-diffusions, and market models. We modified various exponential processes and obtained the equivalent local martingale measures. We obtained the martingales properties and key features and utilized density processes for defining the equivalent changes of measures. As the change of measure was introduced, we studied and managed the stochastic exponentials, predictable characteristics, assessments analyze risk and financial holding, business processes to model, simulate, and compute with the analytics and insights. Furthermore, as the martingales and time series were simplified in integral or summative forms, these computationally tractable results could then be Fast Fourier transformed for real-time predictions and regulatory oversight.