Chapter 65: Applications
651
Exponential processes
Exponential processes; and local martingales; when the exponential
process is a martingale; Brownian motion; converting
semimartingales into martingales by change of law.
652
Lévy processes
Lévy processes and intrinsic Lévy processes; are
semi-martingales; the Cauchy process.
653
Brownian processes
Distributions and characteristic functions; Lévy's
characterization of Brownian motion; locally jump-free local
martingales and time-changed Brownian motion; Brownian-type
processes.
654
Picard's theorem
Doob's quadratic maximal inequality; Picard's theorem for the
Riemann-sum integral; Picard's theorem for the S-integral.
655
The Black-Scholes model
Options, hedging, risk-free processes and a basic pricing model.
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