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Hedging life insurance with pure endowments. (English) Zbl 1183.91067

Summary: We extend the work of M. A. Milevsky, S. D. Promislow and V. R. Young [“Financial valuation of mortality risk via the instantaneous Sharpe ratio”, preprint; available at http://www.ifid.ca/pdf_workingpapers/WP2005NOV4.pdf] and V. R. Young [“Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio”, preprint; available at http://ideas.repec.org/p/arx/papers/0705.1297.html] by pricing life insurance and pure endowments together. We assume that the company issuing the life insurance and pure endowment contracts requires compensation for their mortality risk in the form of a pre-specified instantaneous Sharpe ratio. We show that the price \(P^{m,n}\) for \(m\) life insurances and \(n\) pure endowments is less than the sum of the price \(P^{m,0}\) for \(m\) life insurances and the price \(P^{0,n}\) for n pure endowments. Thereby, pure endowment contracts serve as a hedge against the (stochastic) mortality risk inherent in life insurance, and vice versa.

MSC:

91B30 Risk theory, insurance (MSC2010)
35R60 PDEs with randomness, stochastic partial differential equations
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References:

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