Print Course syllabus
Course syllabus - Differential Equations in Finance
Scope
7.5 credits
Course code
MMA712
Valid from
Autumn semester 2026
Education level
Second cycle
Progressive Specialisation
A1F (Second cycle, has second-cycle course/s as entry requirements)
Main area(s)
Mathematics/Applied Mathematics
Organisation
Department of Business and Mathematics
Ratified
2013-02-01
Revised
2025-11-03
Literature lists
Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.
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Books
Objectives
The aim of the course is to give the students knowledge on how the determination of the prices of financial derivative securities can be reduced to solving boundary value problems for partial differential equations.
Learning outcomes
At the end of the course the student is expected to be able to
- formulate mathematical models for European, American, exotic options and interest rate derivative securities using boundary value problems for partial differential equations.
- explain the difference between classical boundary problems, linear complementarity problems, and free-boundary problems.
- explain the difference between initial, time-dependent and jump conditions.
- solve those of the above mentioned models that admit closed-form solutions.
Course content
Partial differential equations in finance:
Derivation of the classical Black-Scholes equation, transformations on the Black-Scholes equation, American option problems as linear complementarity, free-boundary problems, general equations for derivatives, jump conditions, exotic options: barrier, Asian, look back, multi-asset and some other options, interest rate derivative securities: bonds, some explicit solutions of bonds equations, inverse problem on the market price of risk, applications of bond equations, multifactor interest rate models, two-factor convertible bonds.
Specific requirements
At least totally 120 credits in the engineering, natural sciences, business administration or economics areas where Analytical Finance I 7.5 credits or equivalent is included. In addition, Swedish course 3 or Swedish level 3 and English course 6 or English level 2 are required. For courses given entirely in English exemption is made from the requirement in Swedish course 3 or Swedish level 3.
Examination
Seminar and/or tests, (SEM1) 1.5 credits, marks Pass (G)
Examination, written and/or oral. May be replaced partially or fully by written assignments. (TEN1), 6 credits, marks Pass (G) or Pass with distinction (VG)
A student who has a certificate from MDU regarding disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.
Grade
Three-grade scale