caa a22 4500 465784488 CHVBK 20180323112004.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF01721799 doi (NATIONALLICENCE)springer-10.1007/BF01721799 A monotone variational method for optimal probability distributions [Elektronische Daten] [M. Troutt, T. Paine] Summary: LetI(F) be a functional whereF belongs to a class of distribution functions. In order to find an extremalF, a variational technique is developed which is based upon the fact that positive powers ofF remain probability distributions. The resulting necessary conditions derived from this technique reduce to the Euler-Lagrange equations under the condition that the extremal,F, has a continuous derivative. We apply this technique to certain quadratic functionals, and to the maximum entropy problem. This variational method applies generally to positive bounded, and to positive monotone extremals. This is illustrated by proving that the "stoploss” insurance policy is optimal under standard conditions. Springer-Verlag, 1990 Troutt M. Department of Management, Southern Illinois University at Carbondale, 62901, Carbondale, IL, USA aut Paine T. Department of Mathematics, Southern Illinois University at Carbondale, 62901, Carbondale, IL, USA aut Operations-Research-Spektrum Springer-Verlag 12/4(1990-12-01), 201-206 0171-6468 12:4<201 1990 12 291 https://doi.org/10.1007/BF01721799 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01721799 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Troutt M. Department of Management, Southern Illinois University at Carbondale, 62901, Carbondale, IL, USA aut NATIONALLICENCE 700 1- Paine T. Department of Mathematics, Southern Illinois University at Carbondale, 62901, Carbondale, IL, USA aut NATIONALLICENCE 773 0- Operations-Research-Spektrum Springer-Verlag 12/4(1990-12-01), 201-206 0171-6468 12:4<201 1990 12 291 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer