The course will focus on continuous-time mathematical models for financial markets
1) Continuous-time modeling
The Black and Scholes model and the derivation of the valuation formula, local volatility models and the derivation of the Dupire's formula, stochastic volatility models. Pricing of Asian/American options.
2) Optimization in continuous time models
The Merton Problem and some of its variations, utility maximization in complete markets, martingale methods for investment-consumptions problems.
3) Model ambiguity
Introduction to Martingale Optimal Transport in discrete/continuous time; applications to model-independent super-replication and option prices bounds.
- Docente titolare: Alessandro Doldi
- Docente titolare: Marco Frittelli
- Docente titolare: Marco Maggis