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de Vylder, F.

Maximization, under equality constraints, of a functional of a probability distribution. (English) Zbl 0501.90071

Insur. Math. Econ. 2, 1-16 (1983).
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Cited in 1 Review
Cited in 9 Documents

MSC:

90C15 Stochastic programming
65C99 Probabilistic methods, stochastic differential equations
62P05 Applications of statistics to actuarial sciences and financial mathematics

Keywords:

equality constraints; maximal variance; stop-loss reinsured risk; partial information on the risk; polar function; bipolar function; primal problem; dual problem; effective domain; maximization of probability; distribution functional
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References:

[1] De Vylder, F., Best upper bounds for integrals with respect to measures allowed to vary under conical and integral constraints, Insurance Math. Econom., 1, 2, 109-130 (1982) · Zbl 0488.49030
[2] De Vylder, F. (subm.). Duality theory for bounds on integrals with applications to stop-loss premiums. Submitted for publication.; De Vylder, F. (subm.). Duality theory for bounds on integrals with applications to stop-loss premiums. Submitted for publication. · Zbl 0522.62087
[3] De Vylder, F.; Goovaerts, M., Analytical best upper bounds for stop-loss premiums, Insurance Math. Econom., 1, 3, 197-211 (1982) · Zbl 0508.62088
[4] De Vylder, F.; Goovaerts, M., Maximization of the variance of a stop-loss reinsured risk, Insurance Math. Econom., 2, 2 (1983), to appear · Zbl 0513.62102
[5] Goovaerts, M.; Haezendonck, J.; De Vylder, F., Numerical best bounds on stop-loss premiums, Insurance Math. Econom., 1, 4, 287-302 (1982) · Zbl 0498.62089
[6] Haezendonck, J., De Vylder, F., Delbaen, F. (subm.). Representation theorems for extremal distributions. Submitted for publication.; Haezendonck, J., De Vylder, F., Delbaen, F. (subm.). Representation theorems for extremal distributions. Submitted for publication. · Zbl 0546.60018
[7] Ioffe, A. D.; Tihomirov, V. M., Theory of Extremal Problems (1979), North-Holland: North-Holland Amsterdam · Zbl 0407.90051
[8] Taylor, G. C., Upper bounds on stop-loss premiums under constraints on claim size distribution, Scandinavian Actuarial J., 94-105 (1977) · Zbl 0369.62111
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