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Piecewise linear processes with Poisson‐modulated exponential switching times
Author(s) -
Di Crescenzo Antonio,
Martinucci Barbara,
Ratanov Nikita
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5683
Subject(s) - unobservable , mathematics , jump , exponential function , jump process , lévy process , poisson distribution , piecewise , piecewise linear function , compound poisson process , financial market , poisson process , statistical physics , econometrics , mathematical analysis , statistics , finance , economics , physics , quantum mechanics
We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model.