Lee, Y., & Rheinländer, T. (2023). On the cumulant transforms for Hawkes processes. Journal of Applied Probability, 60(2), 528–541. https://doi.org/10.1017/jpr.2022.96
E105-05 - Forschungsbereich Stochastische Finanz- und Versicherungsmathematik
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Journal:
Journal of Applied Probability
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ISSN:
0021-9002
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Date (published):
Jun-2023
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Number of Pages:
14
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Publisher:
CAMBRIDGE UNIV PRESS
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Peer reviewed:
Yes
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Keywords:
exponentially special semimartingale; Hawkes process; stochastic logarithm
en
Abstract:
We consider the asset price as the weak solution to a stochastic differential equation driven by both a Brownian motion and the counting process martingale whose predictable compensator follows shot-noise and Hawkes processes. In this framework, we discuss the Esscher martingale measure where the conditions for its existence are detailed. This generalizes certain relationships not yet encountered in the literature.
