Introduction to stochastic differential equations with applications to modelling in biology and finance

✍ Scribed by Braumann, Carlos A

• Publisher: Wiley
• Year: 2019
• Tongue: English
• Leaves: 287
• Category: Library

✦ Synopsis

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.  Read more...

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

✦ Subjects

Stochastic differential equations;Biology / Mathematical models;Finance / Mathematical models;MATHEMATICS ;Applied;MATHEMATICS ;Probability et Statistics ;General;Biology ;Mathematical models;Finance ;Mathematical models;Electronic books