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Optimal stopping of a 2-vector risk process. (English) Zbl 1215.60032

Misiewicz, Jolanta K. (ed.), Stability in probability. Selected papers based on the presentations at the 28th international seminar on stability problems for stochastic models, Zakopane, Poland, May 31 – June 5, 2009. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-09-6/pbk). Banach Center Publications 90, 179-191 (2010).
The author considers a problem of double optimal stopping for a marked point process which is related to the asset management of an insurance company. Using the representation of stopping times for piecewise deterministic processes and the method of dynamic programming, a solution is derived for the finite and infinite time horizon model.
For the entire collection see [Zbl 1203.60006].

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
91B30 Risk theory, insurance (MSC2010)
91G50 Corporate finance (dividends, real options, etc.)
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