Chapter 65: Applications
Exponential processes; and local martingales; when the exponential process is a martingale; Brownian motion; converting semimartingales into martingales by change of law.
Distributions and characteristic functions; Lévy's characterization of Brownian motion; locally jump-free local martingales and time-changed Brownian motion.
Doob's quadratic maximal inequality; Picard's theorem for the Riemann-sum integral; Picard's theorem for the S-integral.
The Black-Scholes model
Options, hedging, risk-free processes and a basic pricing model.
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