The aim of this paper is to construct a dynamic programming algorithm for pricing variable annuities with GLWB under a stochastic mortality framework. Although our set-up is very general and only requires the Markovian property for the mortality intensity and the asset price processes, in the numerical implementation of the algorithm we model the former as a non mean reverting square root process, and the latter as an exponential Lévy process. In this way we get a tractable and flexible stochastic model for efficient pricing and risk management of the GLWB. Another contribution of our paper is the verication, through backward induction, of the bang-bang condition for the set of discrete withdrawal strategies of the model. This result is particularly remarkable as in the insurance literature either the existence of optimal bang-bang controls is assumed or it requires suitable conditions. We present extensive numerical examples and compare the results obtained for different market parameters and policyholder behaviours.

Optimal withdrawal strategies in GLWB variable annuities

Anna Rita Bacinello;Rosario Maggistro
;
2022

Abstract

The aim of this paper is to construct a dynamic programming algorithm for pricing variable annuities with GLWB under a stochastic mortality framework. Although our set-up is very general and only requires the Markovian property for the mortality intensity and the asset price processes, in the numerical implementation of the algorithm we model the former as a non mean reverting square root process, and the latter as an exponential Lévy process. In this way we get a tractable and flexible stochastic model for efficient pricing and risk management of the GLWB. Another contribution of our paper is the verication, through backward induction, of the bang-bang condition for the set of discrete withdrawal strategies of the model. This result is particularly remarkable as in the insurance literature either the existence of optimal bang-bang controls is assumed or it requires suitable conditions. We present extensive numerical examples and compare the results obtained for different market parameters and policyholder behaviours.
978-88-5511-310-6
File in questo prodotto:
File Dimensione Formato  
Bacinello_Maggistro_Zoccolan Optimal withdrawal strategies in GLWB.pdf

accesso aperto

Tipologia: Documento in Versione Editoriale
Licenza: Creative commons
Dimensione 597.95 kB
Formato Adobe PDF
597.95 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3018754
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact