Konstantin Izyurov

**Director of the specialization**:

Konstantin Izyurov

**Mandatory core courses**, 10-25 cr

MAST31701 Probability theory I (5 cr)

MAST31702 Probability theory II (5 cr)

MAST30132 Introduction to Real and Fourier Analysis (5 cr) recommended

MAST31002 Functional analysis (10 cr) recommended

**Specialization courses**, at least 10 cr from this list:

MAST31707 Malliavin calculus (10 cr)

MAST31706 Stochastic analysis I (5 cr)

MAST31710 Stochastic analysis II (5 cr)

TCM310 Stochastic methods (10 cr)

MAST31704 Topics in probability I (5 cr)

MAST31705 Topics in probability II (5 cr)

MAST30001 **M****aster's thesis seminar (5 cr)**

MAST31000** Master's thesis (30 cr) (the link includes grading scale and criteria)**

Other advanced courses from the list of core courses, mathematics, applied mathematics, statistics courses and/or courses from other programmes as approved in personal study plan.

Other requirements, such as possibly required bachelor's level mathematics courses (the module 0-35 cr other studies) are explained here:

Konstantin Izyurov

Optional courses: master level courses in Mathematics, Statistics

and/or minor subjects (40-60 cr., of which no more than 30 cr. in minor subjects)

Recommended courses: Stochastic processes, Stochastic analysis, Large deviations, Malliavin calculus, Mathematical finance, Risk theory, Study track courses in Mathematical Physics, Extreme events, other advanced courses in mathematics or statistics

Specialization courses (10–20 credits). It is strongly recommended that to take at least 10 cr. from the following courses: Stochastic processes, Stochastic analysis, Malliavin calculus, Mathematical finance, Risk theory. It is also possible to take a course under the code "Study track Course in Mathematical Physics" if the topic is appropriate (to be agreed with a faculty member).

Other courses in mathematics and statistics: (0-20cr), to be agreed with a faculty member: Vector analysis II, 5cr. Differential equations II 5cr., Statistical inference II 10cr

Example 1

A student inclined to study Probability on advanced level, possibly with a goal to pursue a Ph. D. in the field.

**Year 1, Autumn**

Probability theory I+II

Functional analysis

Mathematical finance I-II

Optimal stochastic control with applications to finance

**Year 1, Spring**

Topics in Probability I+II

Stochastic Analysis I+II

Introduction to mathematical physics

**Year 2, Autumn**

Malliavin calculus

Spectral theory

Topics in mathematical physics

**Year 2, Spring**

Pro gradu seminar and thesis.

Example 2

A student interested in more applied aspects of Stochastics.

**Year 1, Autumn**

Probability theory I+II,

Risk theory

Financial mathematics I+II

Optimal stochastic control with applications to finance

**Year 1, Spring**

Topics in Probability I

Stochastic Analysis I+II

Advanced risk theory

Tariff theory

**Year 2, Autumn**

Malliavin calculus

Life insurance mathematics

Mathematical modelling

**Year 2, Spring**

MAST30001 Master´s thesis seminar and MAST31000 Master´s thesis

**List of stochastic courses:**

MAST31703 Advanced topics in probability (5 cr)

MAST31707 Malliavin calculus (10 cr)

MAST31709 Optimal stochastic control with applications to finance (5 cr)

MAST31701 Probability theory I (5 cr)

MAST31702 Probability theory II (5 cr)

MAST31704 Topics in probability (5 cr)

MAST31705 Topics in probability (5 cr)

MAST31706 Stochastic analysis I (5 cr)

MAST31010 Stochastic analysis II (5 cr)

TCM310 Stochastic methods (10 cr)