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Biagini, Francesca; Groll, Andreas; Widenmann, Jan (2016): Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains. In: Risks, Vol. 4, No. 3, 23


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.