MAX–MIN OPTIMIZATION PROBLEM FOR VARIABLE ANNUITIES PRICING

Christophette Blanchet-Scalliet (), Etienne Chevalier (), Idris Kharroubi () and Thomas Lim ()
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Christophette Blanchet-Scalliet: Institut Camille Jordan, Université de Lyon, Ecole Centrale de Lyon, CNRS UMR 5208 Ecully, France
Etienne Chevalier: LaMME, Université d’Evry Val d’Essonne, UMR CNRS 8071, Evry, France
Idris Kharroubi: CEREMADE, Université Paris Dauphine, CNRS UMR 7534, Crest, Paris, France
Thomas Lim: LaMME, ENSIIE, UMR CNRS 8071 Evry, France

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 08, 1-35

Abstract: In this paper, we study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts, namely guaranteed minimum death benefits and guaranteed minimum living benefits that allow the insured to withdraw money from the associated account. Here, the price of variable annuities corresponds to 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 the indifference fee rate. We focus on the worst case for the insurer, assuming that 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 withdrawal 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 sensitivity.

Keywords: Variable annuities; insurance; indifference pricing; utility maximization; backward stochastic differential equation (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024915500533

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