Ebook: Introduction to stochastic differential equations with applications to modelling in biology and finance
Author: Braumann Carlos A
- Tags: Stochastic differential equations, Biology / Mathematical models, Finance / Mathematical models, MATHEMATICS, Applied, MATHEMATICS, Probability et Statistics, General, Biology, Mathematical models, Finance, Mathematical models, Electronic books
- Year: 2019
- Publisher: Wiley
- Language: English
- pdf
Abstract: 13 Girsanov's theorem13.1 Introduction through an example; 13.2 Girsanov's theorem; 14 Options and the Black-Scholes formula; 14.1 Introduction; 14.2 The Black-Scholes formula and hedging strategy; 14.3 A numerical example and the Greeks; 14.4 The Black-Scholes formula via Girsanov's theorem; 14.5 Binomial model; 14.6 European put options; 14.7 American options; 14.8 Other models; 15 Synthesis; References; Index; End User License Agreement.
10.1 Dynkin's formula10.2 Feynman-Kac formula; 11 Introduction to the study of unidimensional Itô diffusions; 11.1 The Ornstein-Uhlenbeck process and the Vasicek model; 11.2 First exit time from an interval; 11.3 Boundary behaviour of Itô diffusions, stationary densities, and first passage times; 12 Some biological and financial applications; 12.1 The Vasicek model and some applications; 12.2 Monte Carlo simulation, estimation and prediction issues; 12.3 Some applications in population dynamics; 12.4 Some applications in fisheries; 12.5 An application in human mortality rates.
4.3 Some analytical properties4.4 First passage times; 4.5 Multidimensional Wiener processes; 5 Diffusion processes; 5.1 Definition; 5.2 Kolmogorov equations; 5.3 Multidimensional case; 6 Stochastic integrals; 6.1 Informal definition of the Itô and Stratonovich integrals; 6.2 Construction of the Itô integral; 6.3 Study of the integral as a function of the upper limit of integration; 6.4 Extension of the Itô integral; 6.5 Itô theorem and Itô formula; 6.6 The calculi of Itô and Stratonovich; 6.7 The multidimensional integral; 7 Stochastic differential equations