Fair Valuation of Insurance Liability Cash-Flow Streams in Continuous Time: Applications
52 Pages Posted: 27 Nov 2018
Date Written: November 1, 2018
Delong et al. (2018) presented a theory of fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. In this paper, we investigate in detail two practical applications of our theory of fair valuation. In the first example, we consider the fair valuation of a terminal benefit which is contingent on correlated tradeable and non-tradeable financial risks. In the second example, we consider a portfolio of unit-linked contracts contingent on a non-tradeable insurance and a tradeable financial risk. We derive partial differential equations (PDEs) which characterize the continuous-time fair valuation operators in these two examples. We find explicit solutions to the PDEs. The fair values of the liabilities are decomposed into the best estimate of the liability and the risk margin. The arbitrage-free representations of the fair values of the liabilities are also derived. The dynamic hedging strategies associated with the continuous-time fair valuation operators are established. Detailed interpretations of the results, which should be useful both for researchers and practitioners, are provided.
Keywords: Optimal Quadratic Hedging, Actuarial Valuation, Market-Consistent Valuation, Partial Differential Equation, Best Estimate, Risk Margin, Net Asset Value
JEL Classification: C02, G22
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