Multiple-prior Valuation of Cash Flows Subject to Capital Requirements

We study market-consistent valuation of liability cash flows subject to repeated capital requirements 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. For instance, whereas a replicable cash flows is assigned the market value of the replicating portfolio, a cash flow that is not replicable can be assigned a value which can be interpreted as a best estimate plus a risk margin. The latter implies conditions on the conditional risk measures defining capital requirements and on the set of probability measures, priors, defining the valuation functional. Aiming for applicability, we 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.