Piecewise linear processes with Poisson-modulated exponential switching times

Antonio Di Crescenzo; Barbara Martinucci; Nikita Ratanov

doi:10.1002/mma.5683

Piecewise linear processes with Poisson-modulated exponential switching times

Antonio Di Crescenzo, Barbara Martinucci, Nikita Ratanov

Research output: Contribution to journal › Research Article › peer-review

1 Scopus citations

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.

Original language	English (US)
Pages (from-to)	4606-4626
Number of pages	21
Journal	Mathematical Methods in the Applied Sciences
Volume	42
Issue number	13
DOIs	https://doi.org/10.1002/mma.5683
State	Published - Sep 15 2019

All Science Journal Classification (ASJC) codes

General Mathematics
General Engineering

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10.1002/mma.5683

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title = "Piecewise linear processes with Poisson-modulated exponential switching times",

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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AU - Martinucci, Barbara

AU - Ratanov, Nikita

PY - 2019/9/15

Y1 - 2019/9/15

N2 - 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.

AB - 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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DO - 10.1002/mma.5683

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AN - SCOPUS:85067418362

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 13

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Piecewise linear processes with Poisson-modulated exponential switching times

Abstract

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