Course description
Partial differential equations are among the most important modeling and analysis tools in quantitative finance. This goals of the class are:
- The theory of the partial differential equations most used in finance
- The connection between partial differential equations and diffusion processes
- Boundary conditions
- Formulating partial differential equations that solve optimization problems --
Hamilton Jacobi Bellman equations - Formulating and analyzing jump diffusion models
- The Fourier transform and its application to finding special solutions
- Perturbation theory and approximate solutions
Some target applications will be:
- Pricing exotic options with barriers and lookback features
- Explicit solutions of the Heston and Vasicek models
- Merton’s optimal dynamic investment problem
- The optimal liquidation model of Almgren and Chriss
- Treating small factors by perturbation theory