2018/2019

2018/2019

DM270

MAT/06 (PROBABILITY AND MATHEMATICAL STATISTICS)

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

1°

1st semester (01/10/2018 - 18/01/2019)

6

48 lesson hours

Italian

ORAL TEST

CARBONE RAFFAELLA (titolare) - 6 ECTS

The contents of the courses "Probabilita' e Statistica" and "Probabilita"

The aim is to give some fundamental notions about the applications to finance of the theory of probability and of stochastic processes.

Introduction to some basic notions of mathematical finance: markets, options, strategies, options' pricing and hedging. Study of some main properties of markets in a discrete setting and of the Black and Scholes' model.

Extended summary

- Quick resume of some probabilistic tools (conditional expectations and martingales, in particular).
- Definitions of basic objects used in mathematical finance: options, markets, strategies, arbitrage...
- Pricing and hedging european options in discrete models (with discrete times and discrete probability space).
- Brownian motion and elements of stochastic calculus.
- Pricing and hedging european options in the Black and Scholes' model.
- Problems connected to asian and american options.

Lectures about theoretical contents and interactive lectures where students will be called to solve some easy problems.

"Introduction to Stochastic Calculus Applied to Finance", D.Lamberton e B. Lapeyre, Chapman&Hall/CRC

Oral examination. The questions will concern the topics developed during the lectures. The student will have to prove an appropriate comprehension of the subject matter.

Oral examination. The questions will concern the topics developed during the lectures. The student will have to prove an appropriate comprehension of the subject matter.