Neaditivne mere v družbeno ekonomskih vedah : magistrsko delo
Škulj, Damjan
Modeli pričakovane uporabnosti, ki vključujejo običajne aditivne verjetnosti, se v veliko pomembnih primerih izkažejo za neustrezne. To velja predvsem za primere, ko niso znane natančne verjetnosti ...dogodkov ali pa želimo modelirati odnos do tveganja in negotovosti. Nekatere pomanjkljivosti lahko odpravimo, čese odrečemo predpostavki o aditivnosti verjetnosti. Verjetnostno mero na algebri dogodkov pri takem modelu zamenjamo z neko monotono funkcijo ▫$\upsilon :{\cal S} \rightarrow \mathbb R$▫ na množici dogodkov ▫${\cal S}$▫. Tako funkcijo imenujemo kapaciteta. Pričakovane uporabnosti lahko v takem modelu predstavimo s Choquetovim integralom, ki je posplošitev Riemannovega integrala za neaditivne mere. Čeprav Choquetov integral v splošnem ni aditiven, se da nanj posplošiti veliko pomembnih lastnosti Riemannovega integrala. Pomembno vlogo pa igrajo pri Choquetovem integralu tudi nekatere lastnosti, ki jih aditivni integral nima, na primer subaditivnost in superaditivnost, ki sta v neposredni povezavi z odnosom do negotovosti in tveganja.
Type of material - master's thesis
Publication and manufacture - Ljubljana : [D. Škulj], 2001
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