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A two-parameter family of pension contribution functions and stochastic optimization. (English) Zbl 0658.62124

In ibid. 5, 141-146 (1986; Zbl 0587.62191), the author has suggested a linear function of A(t) (present value of future benefits) and F(t) (fund) as pension contribution function in place of the form given in C. L. Trowbridge [Trans. Soc. Actuaries 15, 151-169 (1963)] which is a one-parameter family of funding methods. Here we provide some theoretical justification for such a method by showing that, in the simplified model of this paper, the optimal solution of a stochastic control problem yields, as contribution function, an affine function of A(t) and F(t).

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
93E20 Optimal stochastic control

Citations:

Zbl 0587.62191
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References:

[1] Arnold, L., Stochastic differential equations: theory and applications, (1974), Wiley New York
[2] Bowers, N.L.; Hickman, J.C.; Nesbitt, C.J., Introduction to the dynamics of pension funding, Transactions of the society of actuaries, 28, 177-203, (1976)
[3] Bowers, N.L.; Hickman, J.C.; Nesbitt, C.J., The dynamics of pension function. contribution theory, Transactions of the society of actuaries, 31, 93-119, (1979)
[4] Fleming, W.H.; Rishel, R.W., Deterministic and stochastic optimal control, (1975), Springer-Verlag Berlin · Zbl 0323.49001
[5] Gasiewski, P., A comparative analysis of pension funding methods, ()
[6] O’Brien, T.V., A stochastic-dynamic approach to pension funding, Insurance: mathematics and economics, 5, 141-146, (1986) · Zbl 0587.62191
[7] Trowbridge, C.L., Fundamentals of pension funding, Transactions of the society of actuaries, 4, 17-43, (1952)
[8] Trowbridge, C.L., The unfunded present value family of pension funding methods, Transactions of the society of actuaries, 15, 151-169, (1963)
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