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 ass...

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Bibliographic Details
Published in:Insurance, mathematics & economics Vol. 111; pp. 41 - 56
Main Authors: Engsner, Hampus, Lindskog, Filip, Thøgersen, Julie
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2023
Subjects:
Capital requirements
Insurance valuation
Limited liability
Market-consistent valuation
Market-consistent valuation Insurance valuation Capital requirements Limited liability Optimal stopping
matematisk statistik
Mathematical Statistics
Optimal stopping
Capital requirements
Optimal stopping
Market-consistent valuation
G22
G32
G28
Insurance valuation
Limited liability
ISSN:0167-6687, 1873-5959, 1873-5959
Online Access:Get full text
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Summary: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.
ISSN:0167-6687
1873-5959
1873-5959
DOI:10.1016/j.insmatheco.2023.02.007