Fair valuation of insurance liability cash-flow streams in continuous time: Theory

Łukasz Delong, Jan Dhaene and Karim Barigou

Insurance: Mathematics and Economics, 2019, vol. 88, issue C, 196-208

Abstract: We investigate fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. We first consider one-period hedge-based valuations, where in the first step, an optimal dynamic hedge for the liability is set up, based on the assets traded in the market and a quadratic hedging objective, while in the second step, the remaining part of the claim is valuated via an actuarial valuation. Then, we extend this approach to a multi-period setting by backward iterations for a given discrete-time step h, and consider the continuous-time limit for h→0. We formally derive a partial differential equation for the valuation operator which satisfies the continuous-time limit of the multi-period, discrete-time iterations and prove that this valuation operator is actuarial and market-consistent. We show that our continuous-time fair valuation operator has a natural decomposition into the best estimate of the liability and a risk margin. The dynamic hedging strategy associated with the continuous-time fair valuation operator is also established. Finally, the valuation operator and the hedging strategy allow us to study the dynamics of the net asset value of the insurer.

Keywords: Optimal quadratic hedging; Actuarial valuation; Market-consistent valuation; Fair valuation; Partial differential equation; Best estimate; Risk margin; Net asset value (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:88:y:2019:i:c:p:196-208

DOI: 10.1016/j.insmatheco.2019.07.003

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