# Elements of Stochastic Calculus

llsms2225  2017-2018  Louvain-la-Neuve

Elements of Stochastic Calculus
5 crédits
30.0 h
Q1
Enseignants
Vrins Frédéric;
Langue
d'enseignement
Anglais
Préalables
Mathematics, informatics, probability and statistics at Bachelor level. In particular, the corresponding UCL courses are
• Mons : MQANT1110 (Mathématiques de Gestion I), MQANT1113 (Statistiques et  Probabilité), MQANT1109 (Informatique de gestion)
• LLN : LINGE1114 (Analyse), LINGE1113 (Probabilité),LINGE1225 (algorithmique et programmation en économie et gestion)
Thèmes abordés
1. Part I: Basic probability concepts (probability space, sigma-fields, random variables, distribution, statistics and sampling via Monte Carlo).
2. Part II : Stochastic processes and related concepts.
3. Part III : random walks and Brownian motion.
4. Part IV : stochastic calculus (stochastic integrals, stochastic differential equation, Ito's lemma, Girsanov theorem)
Acquis
d'apprentissage
 A la fin de cette unité d’enseignement, l’étudiant est capable de : 1 During their programme, students of the LSM Master¿s in management or Master¿s in Business engineering will have developed the following capabilities¿ 2.2. Master highly specific knowledge in one or two areas of management : advanced and current research-based knowledge and methods.   2.4. Activate and apply the acquired knowledge accordingly to solve a problem. 3.1. Conduct a clear, structured, analytical reasoning by applying, and eventually adapting, scientifically based conceptual frameworks and models,to define and analyze a problem. 3.5. Produce, through analysis and diagnosis, implemantable solutions in context and identify priorities for action. 6.1. Work in a team : Join in and collaborate with team members. Be open and take into consideration the different points of view and ways of thinking, manage differences and conflicts constructively, accept diversity.

La contribution de cette UE au développement et à la maîtrise des compétences et acquis du (des) programme(s) est accessible à la fin de cette fiche, dans la partie « Programmes/formations proposant cette unité d’enseignement (UE) ».
Contenu
Fundamental mathematical concepts to understand the behavior of systems whose behavior features randomness.
These skills will be extensively used inLLSMS2226 (derivatives pricing)
Méthodes d'enseignement
15 courses of 2h each including programming sessions on R.
Students will be asked to prepare some courses. The objective of the group and home works is to make the concepts more concrete.
Modes d'évaluation
des acquis des étudiants
Continuous evaluation
• Date: Will be specified later
• Type of evaluation:  Teamwork (25%) and individual work (15%)
Evaluation week
• Oral: No
• Written: No
Examination session
• Oral: Yes
• Written: No
• Unavailability or comments: 60% : Made of two parts : a pratical part and a theoretical part
An oral exam (60%) made of two parts :
1. A practical part (test student's skills to apply and use the main concepts)
2. A theoretical part (evaluate the understanding depth).
Teamworks during the year (25%) and an individual work (15%) that will be discussed during the exam.
Bibliographie
Slides, reference books and R code
lectures conseillées :
• Hassler, Stochastic Processes and Calculus: an elementary introductions with applications, Springer 2016
• Mikosh, M. Elementary Stochastic Calculus (with Finance in view), Wolrd Scientific, 1998.
• Joshi, M. : Concepts and Practice of Mathematical Finance, Cambridge University Press, 2003.
• Shreve, S. : Stochastic calculus for Finance I & II, Springer 2004.
Faculté ou entité
en charge
CLSM

#### Programmes / formations proposant cette unité d'enseignement (UE)

Intitulé du programme
Sigle
Crédits
Prérequis
Acquis
d'apprentissage
Master [120] en ingénieur de gestion

Master [120] en sciences économiques, orientation générale

Master [120] en ingénieur de gestion