Abstract
In this chapter we will extend the notion of a Markov bridge to the case when the final bridge condition or the length of the bridge is not known in advance but revealed via an observation of a related process. We will call such a process dynamic Markov bridge. We provide conditions under which such a process exists as a unique solution of an SDE. This construction will be fundamental in solving the Kyle–Back models considered in the second part of the book.
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Notes
- 1.
Recall from Chap. 2 that this implies the existence and uniqueness of a solution, P 0, (x, z), to the associated local martingale problem. In this chapter whenever we refer the solution of the local martingale problem starting from 0 we will drop the reference to the time component and write P x, z instead of P 0, (x, z).
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Çetin, U., Danilova, A. (2018). Dynamic Bridges. In: Dynamic Markov Bridges and Market Microstructure. Probability Theory and Stochastic Modelling, vol 90. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8835-8_5
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DOI: https://doi.org/10.1007/978-1-4939-8835-8_5
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