A new immunization inequality for random streams of assets, liabilities and interest rates

Lesław Gajek and Elżbieta Krajewska

Insurance: Mathematics and Economics, 2013, vol. 53, issue 3, 624-631

Abstract: In this paper, we investigate the problem of immunization of insurers’ surplus when liabilities are financed by a stream of assets. The term structure of interest rates is assumed to be random, as are the streams of assets and liabilities. A new inequality for changes in the portfolio surplus in response to changes in the term structure of interest rates is proven. A comparison with other immunization inequalities shows that it gives better lower bounds for a wide variety of scenarios. The inequality is sharp in the sense that the lower bound is attainable for some interest rate perturbations. Whenever net insurance premiums are considered, it is factorized into a product of two terms: one depending only on the change of interest rates, and the other depending only on the portfolio structure. Hence the second term may be treated as a measure of the interest rate risk. We call it L2-measure, because it is related to the second order distance between assets and liabilities. Explicit formulas for this measure for portfolios of some life products vs streams of net premiums are given. Applications to the Merton’s, Vasicek’s and simple log-normal models of interest rate are also provided.

Keywords: Immunization; Asset–Liability Management; Interest rate risk; Vasicek’s model; Merton’s model (search for similar items in EconPapers)
JEL-codes: G11 G22 G23 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668713001339
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:53:y:2013:i:3:p:624-631

DOI: 10.1016/j.insmatheco.2013.08.012

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().