Unit-linked life insurance policies: Optimal hedging in partially observable market models

Claudia Ceci, Katia Colaneri and Alessandra Cretarola

Insurance: Mathematics and Economics, 2017, vol. 76, issue C, 149-163

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.

Keywords: Unit-linked life insurance contract; Progressive enlargement of filtration; Partial Information; Local risk-minimization; Föllmer–Schweizer decomposition; Markov processes (search for similar items in EconPapers)
JEL-codes: C02 G11 G22 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:76:y:2017:i:c:p:149-163

DOI: 10.1016/j.insmatheco.2017.07.005

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