L��vy 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.