Abstract
We introduce the first of our two key martingales and consider two immediate applications. In the first application, we will use the martingale to construct a change of measure and thereby consider the dynamics of X under the new law. In the second application, we shall use the martingale to study the law of the process \(\overline{X}= \{\overline{X}_{t}\,\colon t\geq 0\}\), where
In particular, we shall discover that the position of the trajectory of \(\overline{X}\), when sampled at an independent and exponentially distributed time, is again exponentially distributed.
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Kyprianou, A.E. (2013). The Wald Martingale and the Maximum. In: Gerber–Shiu Risk Theory. EAA Series. Springer, Cham. https://doi.org/10.1007/978-3-319-02303-8_2
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DOI: https://doi.org/10.1007/978-3-319-02303-8_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02302-1
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