Exponential Martingales and Changes of Measure for Counting Processes

Research output: Contribution to journal › Journal article › Research › peer-review

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Exponential Martingales and Changes of Measure for Counting Processes. / Sokol, Alexander; Hansen, Niels Richard.

In: Stochastic Analysis and Applications, Vol. 33, No. 5, 03.09.2015, p. 823-843.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Sokol, A & Hansen, NR 2015, 'Exponential Martingales and Changes of Measure for Counting Processes', Stochastic Analysis and Applications, vol. 33, no. 5, pp. 823-843. https://doi.org/10.1080/07362994.2015.1040890

APA

Sokol, A., & Hansen, N. R. (2015). Exponential Martingales and Changes of Measure for Counting Processes. Stochastic Analysis and Applications, 33(5), 823-843. https://doi.org/10.1080/07362994.2015.1040890

Vancouver

Sokol A, Hansen NR. Exponential Martingales and Changes of Measure for Counting Processes. Stochastic Analysis and Applications. 2015 Sep 3;33(5):823-843. https://doi.org/10.1080/07362994.2015.1040890

Author

Sokol, Alexander ; Hansen, Niels Richard. / Exponential Martingales and Changes of Measure for Counting Processes. In: Stochastic Analysis and Applications. 2015 ; Vol. 33, No. 5. pp. 823-843.

Bibtex

@article{c94b9e2ec44a4be2a70a63a96dd5cbb9,
title = "Exponential Martingales and Changes of Measure for Counting Processes",
abstract = "We give sufficient criteria for the Dol{\'e}ans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes, counting processes with stochastic intensities depending on diffusion processes as well as inhomogeneous finite-state Markov processes.",
keywords = "Counting process, Exponential martingale, Girsanov, Intensity, Uniform integrability",
author = "Alexander Sokol and Hansen, {Niels Richard}",
year = "2015",
month = sep,
day = "3",
doi = "10.1080/07362994.2015.1040890",
language = "English",
volume = "33",
pages = "823--843",
journal = "Stochastic Analysis and Applications",
issn = "0736-2994",
publisher = "Taylor & Francis",
number = "5",

}

RIS

TY - JOUR

T1 - Exponential Martingales and Changes of Measure for Counting Processes

AU - Sokol, Alexander

AU - Hansen, Niels Richard

PY - 2015/9/3

Y1 - 2015/9/3

N2 - We give sufficient criteria for the Doléans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes, counting processes with stochastic intensities depending on diffusion processes as well as inhomogeneous finite-state Markov processes.

AB - We give sufficient criteria for the Doléans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes, counting processes with stochastic intensities depending on diffusion processes as well as inhomogeneous finite-state Markov processes.

KW - Counting process

KW - Exponential martingale

KW - Girsanov

KW - Intensity

KW - Uniform integrability

U2 - 10.1080/07362994.2015.1040890

DO - 10.1080/07362994.2015.1040890

M3 - Journal article

VL - 33

SP - 823

EP - 843

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

SN - 0736-2994

IS - 5

ER -

ID: 150697509