Kaisa_2012_3_photo by Veikko Somerpuro

Ilmoittaudu
14.8.2017 klo 09:00 - 19.10.2017 klo 23:59

Aikataulu

Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

PäivämääräAikaOpetuspaikka
Ke 6.9.2017
12:15 - 14:00
To 7.9.2017
10:14 - 12:00
Ke 13.9.2017
12:15 - 14:00
To 14.9.2017
10:14 - 12:00
Ke 20.9.2017
12:15 - 14:00
To 21.9.2017
10:14 - 12:00
Ke 27.9.2017
12:15 - 14:00
To 28.9.2017
10:14 - 12:00
Ke 4.10.2017
12:15 - 14:00
To 5.10.2017
10:14 - 12:00
Ke 11.10.2017
12:15 - 14:00
To 12.10.2017
10:14 - 12:00
Ke 18.10.2017
12:15 - 14:00
To 19.10.2017
10:14 - 12:00
To 2.11.2017
09:15 - 12:00

Muu opetus

07.09. - 19.10.2017 To 14.15-16.00
Dario Gasbarra
Opetuskieli: englanti

Materiaalit

Bibliography

Luentomateriaalit

Muu

Tehtävät

Problem sheet 1 (14.9.2017)

Problem sheet 3 (28.9.2017)

Problem sheet 4 (5.10.2017)

Problem sheet 5 (12.10.2017)

Problem sheet 6 (19.10.2017)

Contents

Probabilities as Pricing systems. Options and financial risks.
Elements of convex analysis. Separating hyperplane theorem in finite and infinite dimension.
Abitrage in 1 period market models. Equivalent Risk neutral probabilities, hedging and the first fundamental theorem of asset pricing. Change of numeraire. Incomplete markers and the second fundamental theorem of asset pricing. Superreplication. Multiperiod models, martingales equivalent martingale measures. Hedging in the binomial model by using discrete Malliavin calculus. Stopping times, optimal stopping problem and american options.

Kuvaus

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Probability Theory I .II

Stochastic analysis

Option pricing in discrete time

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

Arbitrage pricing theory and Market completeness. Pricing in incomplete markets. The necessary concepts from convex analysis will be also introduced.

Lecture notes; Föllmer & Schied: Stochastic finance an introduction in discrete time

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later