| EPSRC Reference: |
GR/S05250/01 |
| Title: |
Jump processes in finance with state space dependent distributions: comparisons for transition functions and testing models |
| Principal Investigator: |
Jacob, Professor N |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Swansea University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 2003 |
Ends: |
30 September 2004 |
Value (£): |
23,874
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| EPSRC Research Topic Classifications: |
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| EPSRC Industrial Sector Classifications: |
| Financial Services |
No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Many models in the mathematics of finance use Levy processes, i.e. jump processes. Levy processes have stationary and independent increments which makes their distributions a convolution semigroup. Barndorff-Nielsen and Levendorskii suggested that models should be considered where the distributions are state space dependent. They implemented this by making the parameters of a distribution of a given Levy process state space dependent, which is an ad hoc model and was improved by using very special pseudo-differential operators. In this project it is suggested to start with a pseudo-differential operator q(x,D) such that its symbol q(x,y) is comparable with a fixed characteristic exponent h(y) of a Levy process, and to use a symbolic calculus to compare the distribution of the process generated by -q(x,D) with the distribution of the process generated by -h(D), i.e. a Levy process (freezing coefficients). We will concentrate on some typical examples which in general are not covered by a classical symbol class. Hence the full theory of pseudo-differential operators with negative definite symbols as developed by the principal investigator and his students is needed.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.swan.ac.uk |