PhD course on numerical solution of stochastic differential equations with jumps
10th-11th June 2014
Objectives
The aim of this lecture series is to present various modern numerical methods for stochastic differential equations, including jump diffusions. It develops further mathematical concepts, techniques and intuition necessary for modern modelling of dynamical phenomena such as derivative pricing and risk management in finance. This lecture series provides the foundations for a sufficiently rigorous understanding of advanced numerical methods. Emphasis will be laid on developing skills that allow students to deal with numerical questions related to models involving the simulation of solutions for stochastic differential equations. Questions of numerical stability and convergence will be discussed in detail.
Lecture Slides and Reference Book
Click here for the lecture slides.
The course will be based on the 2010 Springer book “Numerical Solution of Stochastic Differential Equations with Jumps in Finance” by Platen and Bruti-Liberati. The chapters covered and a brief description of their content are listed below:
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Ch 4: Stochastic Expansions |
Presents stochastic Taylor expansions and their application. |
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Ch 5-8: Scenario Simulation |
Introduces strong discrete time approximations for stochastic differential equations for the application in scenario simulation. Jump diffusions are covered. |
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Ch 11-14: Monte Carlo Simulation |
Presents modern techniques for Monte Carlo simulation of stochastic differential equations. |
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Ch 14: Numerical Stability |
The propagation of errors is analysed and stability regions are discussed. |
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Ch 16: Variance Reduction Techniques |
Describes a range of powerful methods that permit significant variance reductions in Monte Carlo simulation. |
Lecturer
Professor Eckhard Platen, University of Technology Sydney
Registration
Deadline for registration is 12th May 2014. Participation in the course is free of charge. Please register by filling in this form. It is recommended to sign up as soon as possible due to a restricted number of participants. Note that the registration is not completed until you recieve an automatically generated confirmation e-mail. Later you will receive a second e-mail from the course organizers with information about whether or not you have been accepted to the course. Registration for the course is now closed.
Location
The course will take place at the "H. C. Ørsted Institut", which is located at Universitetsparken 5, 2100 Copenhagen Ø, Denmark.
Schedule
Lectures will take place between 8.30 and 17.00 on Tuesday 10th and Wednesday 11th June 2014. On Tuesday 10th, we will meet at 8.30 in Auditorium 10 of the "H. C. Ørsted Institut" (Universitetsparken 5, 2100 Copenhagen Ø) for the first lecture. A more detailed schedule may be found here.
Credits
The work load of the course corresponds to 1,5 ECTS.
Participants
The course is primarily aimed at PhD students from SCIENCE but is open to others as well on a first-come, first-served basis.
Organizers
- Nina Munkholt, University of Copenhagen (contact person)
- Professor Michael Sørensen, University of Copenhagen
- Professor Eckhard Platen, University of Technology Sydney