Maximization, under equality constraints, of a functional of a probability distribution

DOI10.1016/0167-6687(83)90002-1zbMath0501.90071OpenAlexW1976428555MaRDI QIDQ1172548

F. Etienne De Vylder

Publication date: 1983

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6687(83)90002-1

zbMATH Keywords

dual problemequality constraintspolar functioneffective domainmaximal variancebipolar functionprimal problemdistribution functionalmaximization of probabilitypartial information on the riskstop-loss reinsured risk

Mathematics Subject Classification ID

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

Related Items (9)

On the randomized Schmitter problem ⋮ Insurance calculations using incomplete information ⋮ Computing best bounds for nonlinear risk measures with partial information ⋮ Worst case risk measurement: back to the future? ⋮ On s-convex bounds for Beta-unimodal distributions with applications to basis risk assessment ⋮ Maximization of the variance of a stop-loss reinsured risk ⋮ Extremal generators and extremal distributions for the continuous \(s\)-convex stochastic orderings ⋮ Best bounds on the stop-loss premium in case of known range, expectation, variance and mode of the risk ⋮ Bound on integrals: Elimination of the dual and reduction of the number of equality constraints

Cites Work

• Unnamed Item
• Representation theorems for extremal distributions
• Maximization of the variance of a stop-loss reinsured risk
• Best upper bounds for integrals with respect to measures allowed to vary under conical and integral constraints
• Numerical best bounds on stop-loss premiums
• Analytical best upper bounds on stop-loss premiums
• Duality theory for bounds on integrals with applications to stop-loss premiums
• Upper bounds on stop-loss premiums under constraints on claim size distribution

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