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Details of Grant 

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:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: Swansea University
Scheme: Standard Research (Pre-FEC)
Starts: 01 April 2003 Ends: 30 September 2004 Value (£): 23,874
EPSRC Research Topic Classifications:
Mathematical Analysis
EPSRC Industrial Sector Classifications:
Financial Services No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
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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Organisation Website: http://www.swan.ac.uk