Levy Processes - And Stochastic Calculus

: Heavy-tailed processes often used to model extreme market volatility. Why Stochastic Calculus is Necessary

: A pure jump process typically used to model arrival times or discrete events. Levy processes and stochastic calculus

: The statistical properties of an increment depend only on the length of the time interval, not when it occurred. : Heavy-tailed processes often used to model extreme

, representing its variation (diffusion), jump measure, and location (drift). Key Examples not when it occurred.

: A specialized version of the chain rule that accounts for the "jumps" in the process.

: Recent research uses Lévy-driven SDEs to improve the performance of non-convex optimization and Bayesian learning algorithms. Lévy Processes and Stochastic Calculus

: Used to change probability measures, a vital step in risk-neutral pricing for options. Real-World Applications