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European Actuarial Journal
Published in: European Actuarial Journal 2/2014

01-12-2014 | Original Research Paper

Mathematical analysis of different approaches for replicating portfolios

Authors: Jan Natolski, Ralf Werner

Published in: European Actuarial Journal | Issue 2/2014

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Abstract

This paper considers the most popular approaches for the construction of replicating portfolios for life insurance liabilities known as cash flow matching and terminal value matching. Solutions to these construction approaches are derived and compared. It is shown that the (unique) solutions have fair value equal to the fair value of liabilities. Then, the problems are generalized by relaxing the requirement of static replication to allow for dynamic investment strategies in the cash account with zero present value. A relationship between the solutions to these generalized problems is established, which sheds new light on the relation of the original problems. Finally, it is proved that the fair values of the optimal solutions to the generalized problems remain equal to the fair value of liabilities.
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Footnotes
1
The Conditional Value-at-Risk is also known as Average Value-at-Risk or Tail-Value at Risk.
 
2
Please note that the specific choice of the numéraire asset is irrelevant for the following exposition.
 
3
Usually, \((\tilde{A}^L-\tilde{A}^F(\alpha ))^2\) is preferred over \(\Big |\tilde{A}^L-\tilde{A}^F(\alpha )\Big |\) for mathematical convenience as well as for practical reasons, see e.g. [10, 11] or [19].
 
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Metadata
Title
Mathematical analysis of different approaches for replicating portfolios
Authors
Jan Natolski
Ralf Werner
Publication date
01-12-2014
Publisher
Springer Berlin Heidelberg
Published in
European Actuarial Journal / Issue 2/2014
Print ISSN: 2190-9733
Electronic ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-014-0094-z

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