Incorporation of Stochastic Policyholder Behavior in Analytical Pricing of GMABs and GMDBs

Marcos Escobar Anel (), Mikhail Krayzler, Franz Ramsauer, David Saunders and Rudi Zagst
Additional contact information
Mikhail Krayzler: risklab GmbH, Allianz Global Investors, Seidlstraße 24-24a, 80335 Munich, Germany
Franz Ramsauer: Chair of Mathematical Finance, Technical University of Munich, Parkring 11, 85748 Garching-Hochbrück, Germany
David Saunders: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada
Rudi Zagst: Chair of Mathematical Finance, Technical University of Munich, Parkring 11, 85748 Garching-Hochbrück, Germany

Risks, 2016, vol. 4, issue 4, 1-36

Abstract: Variable annuities represent certain unit-linked life insurance products offering different types of protection commonly referred to as guaranteed minimum benefits (GMXBs). They are designed for the increasing demand of the customers for private pension provision. In this paper we analytically price variable annuities with guaranteed minimum repayments at maturity and in case of the insured’s death. If the contract is prematurely surrendered, the policyholder is entitled to the current value of the fund account reduced by the prevailing surrender fee. The financial market and the mortality model are affine linear. For the surrender model, a Cox process is deployed whose intensity is given by a deterministic function (s-curve) with stochastic inputs from the financial market. So, the policyholders’ surrender behavior depends on the performance of the financial market and is stochastic. The presented pricing scheme incorporates the stochastic surrender behavior of the policyholders and is only based on suitable closed-form approximations.

Keywords: variable annuities; surrender behavior; closed-form approximation; pricing; affine linear model (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://www.mdpi.com/2227-9091/4/4/41/pdf (application/pdf)
https://www.mdpi.com/2227-9091/4/4/41/ (text/html)

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:gam:jrisks:v:4:y:2016:i:4:p:41-:d:82367

Access Statistics for this article

Risks is currently edited by Mr. Claude Zhang

More articles in Risks from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().