# Dynamic Methods for Economics and Finance

Professor: Leandro Gorno (

`<leandro.gorno AT fgv DOT br>`)**Lectures: Wednesdays 10:30-12:30, Thursdays 11-13.**- Office hours: by appointment.

## News

- 17-Apr-2019: As discussed last week, class today will start at 10:30am.

## Class schedule (tentative)

- Class 1:(10/4) Course presentation, dynamic programming in discrete time.
- Class 2:(11/4) Linearization, dynamic programming in continuous time.
- Class 3 (17/4): More dynamic programming in continuous time. Mathematica basics.
- Class 4 (24/4): Poisson shocks. More Mathematica.
- Class 5 (25/4): More Poisson shocks. Introduction to stochastic calculus.
- Class 6 (2/5): More stochastic calculus. Writing HJBs. Applications.
- Class 7 (8/5): Geometric BM. Solving a SDE. Pricing simple FX contracts.
- Class 8 (9/5): ODEs and PDEs in Mathematica.
- Class 9 (15/5): More on meshes, FEM, and boundary value problems. Optimal stopping.
- Class 10 (16/5): More optimal stopping. Smoothness, noise, and vanishing viscosity.
- Class 11 (22/5): More on smoothness and optimal switching.
- Class 12 (23/5: Tracking distributions (KFEs).
- Class 13:
- Class 14:
- Class 15:
- Class 16:
- Class 17:
- Class 18:

## Syllabus

## Slides

## Additional material

## Additional material

## Mathematica notebooks

A crash course in Mathematica. Preliminary. Last update: April 17th 2019.

## References

**Primary:** Dixit, A.K. and Pindyck R.S. "Inverstment under uncertainty", Princeton University Press (1994)

**Secondary**: Harrison, J.M. "Brownian Models of Performance and Control" Link to Stanford GSB page (Note: this book is a new edition of the older classic "Brownian Motion and Stochastic Flow Systems" (1985) Link to Google books, which used to be online)

Pham, H. "Continuous-time Stochastic Control and Optimization with Financial Applications" Link to Springer

Cvitanic, J. and Zhang, J. "Contract Theory in Continuous-Time Models" Link to Springer

**Related papers**:

**Optimal Unemployment Insurance**Hopenhayn and Nicolini (JPE 1997)**Toward a Theory of Discounted Repeated Games with Imperfect Monitoring**Abreu, Pearce and Stachetti (ECMA 1990)**Aggregation and Linearity in the Provision of Intertemporal Incentives**Holmstrom and Milgrom (ECMA 1987)**A Continuous-Time Version of the Principal: Agent Problem**Sannikov (Restud 2008)**Games with Imperfectly Observable Actions in Continuous Time**Sannikov (ECMA 2007)**Competitive Real Options under Private Information**Gorno and Iachan (working paper)