Multiple-prior valuation of cash flows subject to capital requirements

Abstract

We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. Building on the theory on multiple-prior optimal stopping we propose a valuation functional with sound economic properties that applies to any liability cash flow. Whereas a replicable cash flow is assigned the market value of the replicating portfolio, a cash flow that is not fully replicable is assigned a value which is the sum of the market value of a replicating portfolio and a positive margin. The margin is a direct consequence of considering a hypothetical transfer of the liability cash flow from an insurance company to an empty corporate entity set up with the sole purpose to manage the liability run-off, subject to repeated capital requirements, and considering the valuation of this entity from the owner's perspective taking model uncertainty into account. Aiming for applicability, we consider a detailed insurance application and explain how the optimisation problems over sets of probability measures can be cast as simpler optimisation problems over parameter sets corresponding to parameterised density processes appearing in applications.

On the cost‐of‐capital rate under incomplete market valuation

“…In their particular case of a one-period model, they obtain the formulas (3.6) and (3.8) in our special case where the set M is a singleton. Engsner, Lindskog, and Thøgersen [19] then extend the results from [17] to the case of a more general set M such that results in the one-period special case of [19] essentially coincide with (3.6) and (3.8). A delicate issue studied in [19] is to structure the set M such that the multi-period problem is well-posed.…”

“…Engsner, Lindskog, and Thøgersen [19] then extend the results from [17] to the case of a more general set M such that results in the one-period special case of [19] essentially coincide with (3.6) and (3.8). A delicate issue studied in [19] is to structure the set M such that the multi-period problem is well-posed. A key difference to these works, though, is that we define the risk margin as the value in excess of the expected no-limited-liability-claim, see also the next bullet item.…”