The value of a liability cash flow in discrete time subject to capital requirements

• Published in: Finance and stochastics Vol. 24; no. 1; pp. 125 - 167
• Main Authors: Engsner, Hampus, Lindensjö, Kristoffer, Lindskog, Filip
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020; Springer Nature B.V
• Subjects: Capital requirements; Cash flow; Discrete time; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Insurance; Liability; Management; Market-consistent valuation; Mathematics; Mathematics and Statistics; Optimization; Ownership; Probability Theory and Stochastic Processes; Quantitative Finance; Replicating portfolios; Replication; Statistics for Business; 91G50; Capital requirements; Market-consistent valuation; G22; 91G20; G32; Replicating portfolios; G13; 91B74
• ISSN: 0949-2984; 1432-1122; 1432-1122
• DOI: 10.1007/s00780-019-00408-0

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.