Exponential Martingales and Changes of Measure for Counting Processes
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Exponential Martingales and Changes of Measure for Counting Processes. / Sokol, Alexander; Hansen, Niels Richard.
I: Stochastic Analysis and Applications, Bind 33, Nr. 5, 03.09.2015, s. 823-843.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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