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Stochastic optimization for the ruin probability
Author(s) -
Schäl Manfred
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310305
Subject(s) - reinsurance , first hitting time model , stochastic process , mathematical economics , financial market , stochastic programming , mathematical optimization , investment (military) , dynamic programming , discrete time and continuous time , actuarial science , mathematics , economics , computer science , finance , statistics , politics , political science , law
The Cramér‐Lundberg insurance model is studied where the risk process can be controlled by reinsurance and by investment in a financial market. The performance criterion is the ruin probability. The problem can be imbedded in the framework of discrete‐time stochastic dynamic programming. Basic tools are the Howard improvement and the verification theorem. Explicit conditions are obtained for the optimality of employing no reinsurance and of not investing in the market.