Multiple-prior valuation of cash flows subject to capital requirements

We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. The value assigned to an insurance liability is the consequence of (1) considering a hypothetical transfer of an insurance company's liabilities, and financial assets intended to hedge these liabilities, to an empty corporate entity, and (2) considering the circumstances under which a capital provider would want to achieve and maintain ownership of this corporate entity given limited liability for the owner and that capital requirements have to be met at any time for continued ownership. We focus on the consequences of the capital provider assessing the value of continued ownership in terms of a least favorable expectation of future dividends, meaning that we consider expectations with respect to probability measures in a set of equivalent martingale measures. We show that natural conditions on the set of probability measures imply that the value of a liability cash flow is given in terms of a solution to a backward recursion. Through a life and a non-life insurance example we demonstrate how to make the valuation approach operational.