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MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance

Title data

Cyganowski, Sasha ; Grüne, Lars ; Kloeden, Peter E.:
MAPLE for Jump-Diffusion Stochastic Differential Equations in Finance.
In: Nielsen, Søren S. (ed.): Programming Languages and Systems in Computational Economics and Finance. - Boston : Kluwer Academic Publ. , 2002 . - pp. 441-460 . - (Advances in Computational Economics ; 18 )
ISBN 1-4020-7139-6

Abstract in another language

The occurrence of shocks in the financial market is well known and, since the 1976 paper of the Noble Prize laureate R.C. Merton, there have been numerous attempts to incorporated them into financial models. Such models often result in jump-diffusion stochastic differential equations. This chapter describes the use of MAPLE for such equations, in particular for the derivation of numerical schemes. It can be regarded as an addendum to the chapter in this book by Higham and Kloeden (Paper [8] on Peter Kloeden's page on MAPLE for SDEs), which can be referred to for general background and additional literature on stochastic differential equations and MAPLE.

Further data

Item Type: Article in a book
Refereed: Yes
Additional notes: The paper has two errors in the jump-procedure in Section 4:
The lines
tau:=stats[random, exponential[1]](1):
and
else U:=exp(stats[random, normald[mu,sigma]](1)-1): fi:
must read
tau:=stats[random, exponential[lambda]](1):
and
else U:=exp(stats[random, normald[mu,sigma]](1))-1: fi:
respectively.
Note that the second error affects the simulation results, hence the figures produced by the corrected worksheets now look different. Many thanks to Nick Yannios for reporting these errors!
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Result of work at the UBT: No
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 01 Mar 2021 14:24
Last Modified: 23 Mar 2021 09:13
URI: https://eref.uni-bayreuth.de/id/eprint/63400