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- W3121855538 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 $hto 0$. 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." @default.
- W3121855538 created "2021-02-01" @default.
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- W3121855538 date "2018-01-01" @default.
- W3121855538 modified "2023-09-27" @default.
- W3121855538 title "Fair Valuation of Insurance Liability Cash-Flow Streams in Continuous Time: Theory" @default.
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- W3121855538 doi "https://doi.org/10.2139/ssrn.3276971" @default.
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