Unit-linked life insurance policies: Optimal hedging in partially observable market models |
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Affiliation: | 1. Department of Economics, University “G. D’Annunzio” of Chieti-Pescara, Viale Pindaro, 42, I-65127 Pescara, Italy;2. Katia Colaneri, Department of Economics, University of Perugia, Via Alessandro Pascoli, 20, I-06123 Perugia, Italy;3. Alessandra Cretarola, Department of Mathematics and Computer Science, University of Perugia, Via Luigi Vanvitelli, 1, I-06123 Perugia, Italy;1. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong;2. Faculty of Business and Economics, University of Lausanne, CH-1015 Lausanne, Switzerland;3. Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA 52242-1409, USA;1. University of Brescia, Department of Economics and Management, Via S. Faustino 74/B, 25122 Brescia, Italy;2. University of Siena, Department of Economics and Statistics, Piazza San Francesco 7/8, 53100, Siena, Italy |
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Abstract: | In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. To allow for mutual dependence between the financial and the insurance markets, we use the progressive enlargement of filtration approach. We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor that also influences the mortality rate of the policyholder. We characterize the optimal hedging strategy in terms of the integrand in the Galtchouk–Kunita–Watanabe decomposition of the insurance claim with respect to the minimal martingale measure and the available information flow. We provide an explicit formula by means of predictable projection of the corresponding hedging strategy under full information with respect to the natural filtration of the risky asset price and the minimal martingale measure. Finally, we discuss applications in a Markovian setting via filtering. |
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Keywords: | Unit-linked life insurance contract Progressive enlargement of filtration Partial Information Local risk-minimization Föllmer–Schweizer decomposition Markov processes |
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