Max-Min optimization problem for Variable Annuities pricing

Christophette Blanchet-Scalliet (), Etienne Chevalier (), Idriss Kharroubi and Thomas Lim ()
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Christophette Blanchet-Scalliet: PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique
Etienne Chevalier: LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique
Idriss Kharroubi: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Thomas Lim: LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: We study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts that are the guaranteed minimum death benefits and the guaranteed minimum living benefits ones and that allow the insured to withdraw money from the associated account. As for many insurance contracts, the price of variable annuities consists in a fee, fixed at the beginning of the contract, that is continuously taken from the associated account. We use a utility indifference approach to determine this fee and, in particular, we consider the indifference fee rate in the worst case for the insurer i.e. when the insured makes the withdrawals that minimize the expected utility of the insurer. To compute this indifference fee rate, we link the utility maximization in the worst case for the insurer to a sequence of maximization and minimization problems that can be computed recursively. This allows to provide an optimal investment strategy for the insurer when the insured follows the worst withdrawals strategy and to compute the indifference fee. We finally explain how to approximate these quantities via the previous results and give numerical illustrations of parameter sensibility.

Keywords: Variable annuities; insurance; indifference pricing; backward stochastic differential equation; utility maximization; insurance. (search for similar items in EconPapers)
Date: 2015
New Economics Papers: this item is included in nep-ias and nep-upt
Note: View the original document on HAL open archive server: https://hal.science/hal-01017160v1
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Citations: View citations in EconPapers (1)

Published in International Journal of Theoretical and Applied Finance, 2015, ⟨10.1142/S0219024915500533⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01017160

DOI: 10.1142/S0219024915500533

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