Valuation of insurance liability cash flows from an agency perspective

Valuation of insurance liability cash flows from an agency perspective

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This paper sets out a market-consistent valuation methodology for insurance liabilities with nonreplicable cash flows. An explicit allowance for risks associated with such cash flows is common in modern accounting standards, as well as statutory solvency regimes. The paper also seeks to justify such an allowance from an agency perspective, in the interest of consumer protection. We aim to show that the agency perspective can provide clearer guidance as to the purpose of an explicit buffer for non-replicable cash flows, as well as how it may be valued. We define the market-consistent value of a liability cash flow in discrete time subject to repeated capital requirements in accordance with the principles of the Solvency II regulation by considering a hypothetical transfer of the liability to an external insurer, similarly to what was considered in [4], [1] and [2]. We focus both on theoretical aspects of the valuation concerning market-consistency and the effects of filtrations, quantifying the information flows, and practical aspects such as computability for an insurer who is only able to simulate liability cash flows without being able to express the cash flow model analytically.

 

[1] Engsner, H., Lindholm, M. and Lindskog, F. (2017), “Insurance valuation: a computable multiperiod cost-of-capital approach.” Insurance: Mathematics and Economics, vol. 72, pp. 250-264.

[2] Engsner, H., Lindensjö, K. and Lindskog, F. (2018), “The value of a liability cash flow in discrete time subject to capital requirements.”  ar Xiv:1808.03328v1.

[3] Engsner, H., Lindskog, F. and Skrutkowski, M. (2019), “Valuation of insurance liability cash flows from an agency perspective.” Current work.

[4] Möhr, C. (2011) “Market-consistent valuation of insurance liabilities by cost of capital.” ASTIN Bulletin, vol. 41, pp. 315-341.

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