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TRANSFORM ANALYSIS FOR POINT PROCESSES AND APPLICATIONS IN CREDIT RISK
Author(s) -
Giesecke Kay,
Zhu Shilin
Publication year - 2013
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2011.00512.x
Subject(s) - laplace transform , two sided laplace transform , mellin transform , valuation (finance) , point process , portfolio , point (geometry) , credit risk , inverse laplace transform , mathematics , computer science , mathematical optimization , econometrics , fourier transform , actuarial science , economics , mathematical analysis , financial economics , finance , fractional fourier transform , statistics , fourier analysis , geometry
This paper develops a formula for a transform of a vector point process with totally inaccessible arrivals. The transform is expressed in terms of a Laplace transform under an equivalent probability measure of the point process compensator. The Laplace transform of the compensator can be calculated explicitly for a wide range of model specifications, because it is analogous to the value of a simple security. The transform formula extends the computational tractability offered by extant security pricing models to a point process and its applications, which include valuation and risk management problems arising in single‐name and portfolio credit risk.