Theory and Validation of Replicating Portfolios in Insurance Risk Management

31 Pages Posted: 30 Jan 2015 Last revised: 17 Apr 2016

See all articles by Eric Beutner

Eric Beutner

Maastricht School of Business and Economics

Antoon Pelsser

Maastricht University; Netspar

Janina Schweizer

Maastricht School of Business and Economics

Date Written: March 20, 2016

Abstract

The Solvency II framework challenges insurers to evaluate and manage their embedded balance sheet risks appropriately. However, insurances hold balance sheet items, for which closed-form solutions and market prices are not available. Pure Monte Carlo valuation requires nested simulations, which are too time-intensive. Therefore, methods that project these balance sheet items into functional representations, which simplify and enhance risk analysis, have been suggested. Among these, replicating portfolios are widely applied in practice, though their validity and properties have not been fully examined yet. This paper corrects this shortcoming and proposes a mathematical framework within which the asymptotic properties of replicating portfolios are analyzed. It is shown that the replicating portfolio problem is mathematically well-defined and asymptotically converges to the true solution. Hence, this paper provides a general mathematical validation for replicating portfolios applied in insurance. A typical path-dependent insurance policy is discussed within the framework and numerical results are presented.

Keywords: Portfolio replication, Series estimation, Least Squares Monte Carlo, Least squares regression, participating life insurance policy

JEL Classification: G22, C15, G11

Suggested Citation

Beutner, Eric and Pelsser, Antoon A. J. and Schweizer, Janina, Theory and Validation of Replicating Portfolios in Insurance Risk Management (March 20, 2016). Available at SSRN: https://ssrn.com/abstract=2557368 or http://dx.doi.org/10.2139/ssrn.2557368

Eric Beutner

Maastricht School of Business and Economics ( email )

P.O. Box 616
Maastricht, 6200MD
Netherlands

Antoon A. J. Pelsser

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Janina Schweizer (Contact Author)

Maastricht School of Business and Economics ( email )

P.O. Box 616
Maastricht, 6200MD
Netherlands

Register to save articles to
your library

Register

Paper statistics

Downloads
203
rank
144,508
Abstract Views
588
PlumX Metrics