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Monte Carlo Methods for Adaptive Disorder Problems

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Numerical Methods in Finance

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 12))

Abstract

We develop a Monte Carlo method to solve continuous-time adaptive disorder problems. An unobserved signal X undergoes a disorder at an unknown time to a new unknown level. The controller’s aim is to detect and identify this disorder as quickly as possible by sequentially monitoring a given observation process Y. We adopt a Bayesian setup that translates the problem into a two-step procedure of (1) stochastic filtering followed by (2) an optimal stopping objective. We consider joint Wiener and Poisson observation processes Y and a variety of Bayes risk criteria. Due to the general setting, the state of our model is the full infinite-dimensional posterior distribution of X. Our computational procedure is based on combining sequential Monte Carlo filtering procedures with the regression Monte Carlo method for high-dimensional optimal stopping problems. Results are illustrated with several numerical examples.

MSC codes: 60G35 (primary), 60G40, 62C10, 62L15

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Acknowledgements

Assistance with the computational examples was provided by Chunhsiung Lu. I am grateful to two anonymous referees for numerous helpful comments and to Jarad Niemi for many discussions on SMC methods.

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Correspondence to Michael Ludkovski .

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Ludkovski, M. (2012). Monte Carlo Methods for Adaptive Disorder Problems. In: Carmona, R., Del Moral, P., Hu, P., Oudjane, N. (eds) Numerical Methods in Finance. Springer Proceedings in Mathematics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25746-9_3

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