A Large-Scale Optimization Model for Replicating Portfolios in the Life Insurance Industry

44 Pages Posted: 4 Feb 2016

See all articles by Maximilian Adelmann

Maximilian Adelmann

University of Zurich, Students ; University of Zurich - Department of Business Administration

Lucio Fernandez Arjona

Zurich Insurance Group

Janos Mayer

University of Zurich - Institute of Business Administration

Karl Schmedders

University of Zurich

Date Written: January 5, 2016

Abstract

Replicating portfolios have recently emerged as an important tool in the life insurance industry, used for the valuation of companies' liabilities. This paper presents a replicating portfolio (RP) model for approximating life insurance liabilities as closely as possible. We minimize the L1 error between the discounted life insurance liability cash flows and the discounted RP cash flows over a multi-period time horizon for a broad range of different future economic scenarios. We apply two different linear reformulations of the L1 problem to solve large-scale RP optimization problems and also present several out-of-sample tests for assessing the quality of RPs. A numerical application of our RP model to empirical data sets demonstrates that the model delivers RPs that match the liabilities rather closely. The numerical analysis demonstrates that our model delivers RPs with excellent practical properties in a reasonable amount of time. We complete the paper with a description of an implementation of the RP model at a global insurance company.

Keywords: Insurance regulation; liability cash flows; linear programming; out-of-sample tests; replicating portfolios; Solvency II

JEL Classification: C61, C65

Suggested Citation

Adelmann, Maximilian and Fernandez Arjona, Lucio and Mayer, Janos and Schmedders, Karl, A Large-Scale Optimization Model for Replicating Portfolios in the Life Insurance Industry (January 5, 2016). Swiss Finance Institute Research Paper No. 16-04. Available at SSRN: https://ssrn.com/abstract=2727281 or http://dx.doi.org/10.2139/ssrn.2727281

Maximilian Adelmann

University of Zurich, Students ( email )

Zurich
Switzerland

University of Zurich - Department of Business Administration ( email )

Rämistrasse 71
Zurich, CH-8006
Switzerland

Lucio Fernandez Arjona

Zurich Insurance Group ( email )

P.O. Box
Mythenquai 2
Zürich, 8022
Switzerland

Janos Mayer

University of Zurich - Institute of Business Administration ( email )

Moussonstrasse 15
Zurich, CH-8044
Switzerland

Karl Schmedders (Contact Author)

University of Zurich ( email )

Moussonstrasse 15
Zürich, CH-8044
Switzerland
+41 (0)44 634 3770 (Phone)

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