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Stochastic optimal control of annuity contracts. (English) Zbl 1103.91346
Summary: The purpose of this paper is to show how stochastic optimal control theory can be applied to find an optimal investment policy before and after retirement in a defined contribution pension plan where benefits are paid under the form of annuities; annuities are supposed to be guaranteed during a certain fixed period of time. Using different kinds of utility functions we try to look at different strategies on the one hand in the investment part (i.e. before retirement) and on the other hand in the payment part (i.e. after retirement). The needed change of strategy after retirement can be interpreted in this model as a typical ALM constraint taking into account a guaranteed technical interest rate used by the insurer.

##### MSC:
 91G10 Portfolio theory 91B30 Risk theory, insurance (MSC2010) 93E20 Optimal stochastic control
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##### References:
 [1] Blake, D., Pension schemes as options on pension fund assets: implications for pension fund management, Insurance: mathematics and economics, 23, 263-286, (1998) · Zbl 0920.62130 [2] Booth, P.; Yakoubov, Y., Investment for defined contribution pension scheme members close to retirement: an analysis of the “lifestyle” concept, North American actuarial journal, 4, 2, 1-19, (2000) · Zbl 1083.91527 [3] Boulier, J.F.; Huang, S.J.; Taillard, G., Optimal management under stochastic interest, Insurance: mathematics and economics, 28, 173-189, (2001) · Zbl 0976.91034 [4] Bowers, N., Gerber, H., Hickman, Jones, Nesbitt, 1986. Actuarial Mathematics. The Society of Actuaries. [5] Cairns, A., Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time, ASTIN bulletin, 30, 1, 19-55, (2000) · Zbl 1018.91028 [6] Charupat, N.; Milevsky, M., Optimal asset allocation in life annuities, Insurance: mathematics and economics, 30, 199-209, (2002) · Zbl 1074.91548 [7] Deelstra, G.; Grasselli, M.; Koehl, P.F., Optimal investment strategies in a CIR framework, Journal of applied probability, 37, 1-12, (2000) · Zbl 0989.91040 [8] Haberman, S.; Sung, J.H., Dynamic approaches to pension funding, Insurance: mathematics and economics, 15, 151-162, (1994) · Zbl 0818.62091 [9] Haberman, S.; Vigna, E., Optimal investment strategy for defined contribution pension schemes, Insurance: mathematics and economics, 28, 233-262, (2001) · Zbl 0976.91039 [10] Keel, A.; Muller, H.H., Efficient portfolios in the asset liability context, ASTIN bulletin, 25, 33-48, (1995) [11] Menoncin, F., Optimal portfolio and back ground risk: an exact and an approximated solution, Insurance: mathematics and economics, 31, 249-265, (2002) · Zbl 1055.91054 [12] Merton, R.C., Lifetime portfolio selection under uncertainty: the continuous time case, Review of economics and statistics, 51, 247-257, (1969) [13] Merton, R.C., Optimal consumption and portfolio rules in a continuous-time model, Journal of economic theory, 3, 373-413, (1971) · Zbl 1011.91502 [14] Oksendal, B., 1998. Stochastic Differential Equations. Springer, Berlin. · Zbl 0897.60056 [15] Wilkie, A.D., Portfolio selection in the presence of fixed liabilities, Journal of the institute of actuaries, 112, 229-277, (1985) [16] Wise, A., The matching of assets to liabilities, Journal of the institute of actuaries, 111, 445-501, (1984) [17] Zimbidis, A., 2001. Dynamic simultaneous management of financial and longevity risks in a stochastic environment. In: Proceedings of the Congress IME, 2001.
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