We study the decision theory of a maximally risk-averse investor --- one whose objective, in the face of stochastic uncertainties, is to minimize the probability of ever going broke. With a view to developing the mathematical basics of such a theory, we start with a very simple model and obtain the following results: a characterization of best play by investors; an explanation of why poor and rich players may have different best strategies; an explanation of why expectation-maximization is not necessarily the best strategy even for rich players. For computation of optimal play, we show how to apply the Value Iteration method, and prove a bound on its convergence rate.
@InProceedings{berger_et_al:LIPIcs.FSTTCS.2008.1741, author = {Berger, Noam and Kapur, Nevin and Schulman, Leonard and Vazirani, Vijay}, title = {{Solvency Games}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {61--72}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-08-8}, ISSN = {1868-8969}, year = {2008}, volume = {2}, editor = {Hariharan, Ramesh and Mukund, Madhavan and Vinay, V}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1741}, URN = {urn:nbn:de:0030-drops-17419}, doi = {10.4230/LIPIcs.FSTTCS.2008.1741}, annote = {Keywords: Decision making under uncertainity, multi-arm bandit problems, game theory} }
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