Piecewise linear processes with Poisson-modulated exponential switching times

Antonio Di Crescenzo; Barbara Martinucci; Nikita Ratanov

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arXiv · 2103.06680

Piecewise linear processes with Poisson-modulated exponential switching times

Antonio Di Crescenzo·Barbara Martinucci·Nikita Ratanov

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Abstract

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.

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Antonio Di Crescenzo, Barbara Martinucci, Nikita Ratanov. 2021-03-11. Piecewise linear processes with Poisson-modulated exponential switching times. https://arxiv.org/abs/2103.06680

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