Multiple-prior valuation of cash flows subject to capital requirements

TL;DR

This paper introduces a market-consistent valuation method for insurance liabilities that accounts for model uncertainty and regulatory capital requirements, combining replicable and non-replicable cash flows with a margin.

Contribution

It proposes a novel valuation functional based on multiple-prior optimal stopping, applicable to any liability cash flow, incorporating model uncertainty and regulatory considerations.

Findings

Valuation includes a margin for non-replicable cash flows.

The approach models the transfer of liabilities to a dedicated entity.

Optimization problems are simplified via parameterized density processes.

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.