Roberts A.J. Elementary Calculus of Financial Mathematics

© 2009 by the Society for Industrial and Applied Mathematics.
Contents.
Preface.
List of Algorithms.
Financial Indices Appear to Be Stochastic Processes.
Brownianmotionis alsocalledaWienerprocess.
Stochastic drift and volatility are unique.
Basic numerics simulate anSDE.
A binomial lattice prices call option.
Summary.
Exercises.
Ito’s Stochastic Calculus Introduced.
Multiplicative noise reduces exponential growth.
Ito’s formulasolves someSDEs.
The Black–Scholes equation prices options accurately.
Summary.
Exercises.
The Fokker–Planck Equation Describes the Probability Distribution.
The probability distribution evolves forward in time.
Stochasticallysolvedeterministicdifferentialequations.
The Kolmogorov backward equation completes the picture.
Summary.
Exercises.
Stochastic Integration Proves Ito’s Formula.
The Ito integral _b.
afdW.
TheItoformula.
Summary.
Exercises.
Appendix A Extra MATLAB/SCILAB Code.
Appendix B Two Alteate Proofs.
B Fokker–Planckequation.