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The value of a liability cash flow in discrete time subject to capital requirements
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-0775-9680
2020 (English)In: Finance and Stochastics, ISSN 0949-2984, E-ISSN 1432-1122, Vol. 24, no 1, p. 125-167Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the presented approach is based on a hypothetical transfer of the original liability and a replicating portfolio to an empty corporate entity, whose owner must comply with repeated one-period capital requirements but has the option to terminate the ownership at any time. The value of the liability is defined as the no-arbitrage price of the cash flow to the policyholders, optimally stopped from the owner’s perspective, taking capital requirements into account. The value is computed as the solution to a sequence of coupled optimal stopping problems or, equivalently, as the solution to a backward recursion.

Place, publisher, year, edition, pages
2020. Vol. 24, no 1, p. 125-167
Keywords [en]
Market-consistent valuation, Replicating portfolios, Capital requirements
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-161902DOI: 10.1007/s00780-019-00408-0ISI: 000511748200004OAI: oai:DiVA.org:su-161902DiVA, id: diva2:1262537
Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2020-03-02Bibliographically approved
In thesis
1. Multi-period valuation of insurance liabilities subject to capital requirements
Open this publication in new window or tab >>Multi-period valuation of insurance liabilities subject to capital requirements
2018 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In the papers presented here, approaches to multi-period valuation of a liability cashflow in runoff, subject to repeated capital requirements, are developed and analyzed. The valuation approaches are inspired by current risk-based regulatory frameworks for the insurance industry, and consistent with the fundamental principles underlying them. The capital requirements are partly financed by capital providers with limited liability, meaning that the capital providers cannot lose more than the provided capital. Limited liability is an essential ingredient in the considered multi-period valuation framework.

In the first paper, multi-period cost-of-capital valuation is considered. The liability value is defined in terms of the capital provider's criterion for accepting to provide capital which gives rise to a backward recursion from which the liability value can be computed. Explicit solutions to the recursion are obtained when the cashflows can be expressed in terms of multivariate Gaussian distributions.

The second paper recognizes that due to limited liability (an option to default) the cashflow to the capital provider can be seen as that of a financial derivative instrument with optionality. Arbitrage-free valuation of this cashflow, similar to the valuation of so-called American type contingent claims, forms the basis of the multi-period approach to liability cashflow valuation considered here. The issue of selection of a replicating portfolio for offsetting the hedgeable part of the liability cashflow is investigated.

The first two papers consider cashflows and valuations at a fixed set of times to be interpreted as the years from current time until the runoff of the liability is complete. In the third paper, the valuation and cashflow times are allowed to be arbitrary in the form of an arbitrary partition of the entire runoff period. The focus here is to properly define and analyze the effects of letting the mesh of the partition tend to zero, exploring the continuous-time value processes that appear.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2018. p. 115
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:su:diva-161949 (URN)
Presentation
2018-12-03, Hus 6, rum 306, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Opponent
Supervisors
Available from: 2018-11-14 Created: 2018-11-12 Last updated: 2018-11-14Bibliographically approved

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