Stable allocations of risk

Abstract

Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games. We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games. JEL: C 71Keywords: Abstract Measuring risk can be axiomatized by the concept of coherent measures of risk. A risk environment specifies some individual portfolios' realization vectors and a coherent measure of risk. We consider sharing the risk of the aggregate portfolio by studying transferable utility cooperative games: risk allocation games.We show that the class of risk allocation games coincides with the class of totally balanced games. As a limit case the aggregate portfolio can have the same payoff in all states of nature. We prove that the class of risk allocation games with no aggregate uncertainty coincides with the class of exact games.

Capital Allocation in the Insurance Sector

“…Denault 2001;Csóka et al 2009, Csóka andPintér 2016), option pricing (e.g. Myers -Read 2001;Sherris 2006;Kim -Hardy 2007) or other statistical approaches (e.g.…”

Tőkeallokáció a biztosítási szektorban

“…Denault 2001;Csóka et al 2009, Csóka és Pintér 2016 Balog Dóra a témában olyan áttekintést nyújtani, amely gyakorlati oldalról közelíti meg a tő-keallokáció kérdését, a biztosítási szektorra koncentrálva.…”

On the Impossibility of Fair Risk Allocation

“…A totally balanced game has a non-empty core in each of its subgames, where a subgame is obtained by considering only a subset of the players. Csóka et al (2009) show that the class of risk allocation games (using coherent measures of risk) coincides with the class of totally balanced games, that is for any risk allocation game there is a core allocation (a stable way to allocate risk using an allocation rule satisfying Core Compatibility) and any totally balanced game can be generated by a properly chosen risk allocation game. Csóka et al (2009) also prove that the class of risk allocation games with no aggregate uncertainty equals the class of exact games (Schmeidler, 1972), where for each coalition there is a core allocation allocating the stand-alone value of the coalition.…”