ISCTE-IUL > Education > MMF

Equações com Derivados Parciais em Finanças (2 º Sem 2017/2018)

Code:	M7602
Acronym:	M7602
Level:	2nd Cycle
Basic:	No
Teaching Language(s):	Portuguese
Friendly languages:

Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.

Semester	ECTS Credits	Theoretical Lesson (T)	Theoretical and Pratical Lesson (TP)	Practical and laboratorial lesson (PL)	Seminary (S)	Field Work (TC)	Training Period (E)	Tutorial Orientation (OT)	Contact Hours	Autonomous Work	Others (O)	Total Load Hours [?]Contact Hours + Autonomous Work
1	7.0	25.0 h/sem	10.0 h/sem	0.0 h/sem	0.0 h/sem	0.0 h/sem	0.0 h/sem	0.0 h/sem	35.0 h/sem	161.0 h/sem	0.0 h/sem	196.0 h/sem


Since year	2012/2013
Pre-requisites	No
Objectives	This course is gives basic knowledge in partial differential equations, with emphasis in the type of equations commonly used in the pricing of derivative products.
Program	I. Ordinary Differential Equations: First order equations: separation of variables and linear equations. Second order equations: initial conditions and boundary value problems. II. First order Partial Differential Equations (two variables): Example: transport equation. Planar vector fields and integral curves. Method of characteristics. III. Second order linear Partial Differential Equations (two variables): Examples: heat equation, wave equation, Laplace equation. Other examples: Reaction-Diffusion equations; Black-Scholes equation. Classification: characteristics and canonical forms. Boundary and initial conditions. Method of separation of variables. Fourier series. Solution of the heat equation in a bounded interval. Fourier integral. Solution of the heat equation in an unbounded interval. Solution of the Black-Sholes equation for a European option. Notion of free boundary and the price of an American option.
Evaluation Method	Regular grading system: - One written exam with a worth of 100 Students that fail or want to improve their grade in the regular grading system have one additional moment to pass: a re-sit exam, which is worth 100% of the final grade. In any of the evaluation systems (regular or re-sit exam) it is considered that a student has course approval if he has a grade equal or above 9.5 points.
Teaching Method	The student should acquire analytical, information gathering, written and oral communication skills, through the following learning methodologies (LM): 1. Expositional, to the presentation of the theoretical reference frames 2. Participative, with analysis and resolution of application exercises 3. Active, with the realization of individual works 4. Self-study, related with autonomous work by the student, as is contemplated in the Class Planning.
Observations
Basic Bibliographic	Bleecker, D. ; Csordas, G. - Basic Partial Differential Equa- tions, International Press (2003) Brown, J.W. ; Churchill, R. - Fourier Series and Boundary Value Problems , McGraw-Hill, 7a ed. (2006) Farlow, S.J. - Partial Differential Equations for Scientists and En- gineers, Dover (1993)
Complementar Bibliographic	Basov, S. - Partial Differential Equations in Economics and Fi- nance, Nova Science (2007) Wilmott, P. ; Howison, S. ; Dewynne, J. - The Mathematics of Financial Derivatives: A Student Introduction, Cambridge University Press (1995) Zachmanoglou, C.C. ; Thoe, D.W. - Introduction to Partial Dif- ferential Equations with Applications, Dover (1986)