Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains

Francesca Biagini, Andreas Groll and Jan Widenmann
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Francesca Biagini: Department of Mathematics, University of Munich, Theresienstraße 39, 80333 Munich, Germany
Andreas Groll: Department of Statistics, University of Munich, Akademiestr.1, 80799 Munich, Germany
Jan Widenmann: BMW Financial Services, BMW Bank GmbH, 80787 Munich, Germany

Risks, 2016, vol. 4, issue 3, 1-26

Abstract: We study risk-minimization for a large class of insurance contracts. Given that the individual progress in time of visiting an insurance policy’s states follows an F -doubly stochastic Markov chain, we describe different state-dependent types of insurance benefits. These cover single payments at maturity, annuity-type payments and payments at the time of a transition. Based on the intensity of the F -doubly stochastic Markov chain, we provide the Galtchouk-Kunita-Watanabe decomposition for a general insurance contract and specify risk-minimizing strategies in a Brownian financial market setting. The results are further illustrated explicitly within an affine structure for the intensity.

Keywords: insurance liabilities; doubly stochastic Markov chains; risk minimization; MSC; 60J27; 62P05; 91G99; JEL; C02 (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2016
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