Stochastic Methods Field of study: Mathematics
Programme code: W4-N2MT19.2025

Module name: Stochastic Methods
Module code: W4-MT-N2-25-MSto
Programme code: W4-N2MT19.2025
Semester: winter semester 2025/2026
Language of instruction: Polish
Form of verification: course work
ECTS credits: 6
Purpose and description of the content of education:
Celem przedmiotu jest pogłębienie wiedzy z zakresu metod analizy stochastycznej oraz wskazanie jej zastosowań w matematyce finansowej. Treści programowe: 1. Warunkowa wartość oczekiwana. Martyngały. 2. Całka stochastyczna. Wzór Ito. 3. Równania stochastyczne. 4. Zastosowania w matematyce finansowej.
List of modules that must be completed before starting this module (if necessary): not applicable
Learning outcome of the module Codes of the learning outcomes of the programme to which the learning outcome of the module is related [level of competence: scale 1-5]
posiada pogłębioną wiedzę z zakresu metod stochastycznych [MSto _1]
 K_W01 [4/5]
posiada wiedzę na temat roli i znaczenia konstrukcji rozumowań matematycznych wykorzystywanych w metodach stochastycznych [MSto _2]
 K_W02 [4/5]
potrafi analizować modele stochastyczne stosowane w naukach ekonomicznych [MSto _3]
 K_U07 [3/5]
posiada umiejętności wyrażania matematycznych treści związanych z metodami stochastycznymi, w mowie i na piśmie, w tekstach matematycznych o różnym charakterze [MSto _4]
 K_U05 [4/5]
osiada umiejętność weryfikacji poprawności wnioskowania w formalnych dowodach pojawiających się w teorii metod stochastycznych [MSto _5]
 K_U03 [4/5]
zna pojęcia i metody procesów stochastycznych i potrafi je stosować w zagadnieniach praktycznych [MSto _6]
 K_W04 [4/5] K_U07 [4/5]
rozpoznaje struktury matematyczne w wybranych teoriach nauk przyrodniczych [MSto_7]
 K_W04 [1/5]
potrafi stosować procesy stochastyczne jako narzędzie do modelowania zjawisk i analizy ich ewolucji [MSto_8]
 K_U07 [3/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [MSto_fns_1] 15 Formal lecture/ course-related lecture [a01]  course work MSto _1 MSto _2 MSto _3 MSto _6 MSto_7 MSto_8
discussion classes [MSto_fns_2] 15 Activating method – peer learning [b08] 
Laboratory exercise / experiment [e01]  		course work MSto _1 MSto _2 MSto _3 MSto _4 MSto _5 MSto _6 MSto_7 MSto_8
The student's work, apart from participation in classes, includes in particular:
Name Category Description
Literature reading / analysis of source materials [a02] Preparation for classes
reading the literature indicated in the syllabus; reviewing, organizing, analyzing and selecting source materials to be used in class
Developing practical skills [a03] Preparation for classes
activities involving the repetition, refinement and consolidation of practical skills, including those developed during previous classes or new skills necessary for the implementation of subsequent elements of the curriculum (as preparation for class participation)
Consulting materials complementary to those indicated in the syllabus [a04] Preparation for classes
agreeing on materials complementary to those indicated in the syllabus, supporting the implementation of tasks resulting from or necessary for class participation
Verification / adjustment / discussion of syllabus provisions [b02] Consulting the curriculum and the organization of classes
consulting the content of the syllabus, possibly in the presence of the year tutor or members of the class group, and, if necessary, reassessing the provisions concerning special conditions for class participation, e.g., space and time requirements, technical and other requirements, including conditions for participation in classes outside the walls of the university, classes organized in blocks, organized online, etc.
Determining the stages of task implementation contributing to the verification of learning outcomes [c01] Preparation for verification of learning outcomes
devising a task implementation strategy embracing the division of content, the range of activities, implementation time and/or the method(s) of obtaining the necessary materials and tools, etc.
Studying the literature used in and the materials produced in class [c02] Preparation for verification of learning outcomes
exploring the studied content, inquiring, considering, assimilating, interpreting it, or organizing knowledge obtained from the literature, documentation, instructions, scenarios, etc., used in class as well as from the notes or other materials/artifacts made in class
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)