Actuaries intuitively feel that positive correlations between individua.l risks reveal a more dangerous situation compared to independence. Tlw purposp of this short note is to formalize this natural idea. Specifically, it is showll that the sum of risks exhibiting a weak form of dependenc:e known as positive cumulative dependence is larger in convex order than the c:oITespondiIl~ sUln under the theoretic:al independence assumption.

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We study cooperative solutions for differential games where players consume a common property resource. Players are asymmetric, in the sense that they have different preferences and, in particular, different time preferences. We propose a new time-consistent dynamic bargaining procedure for this class of games. This solution concept, which is defined as the time-consistent dynamic bargaining (TCB) solution, extends the recursive Nash bargaining solution introduced in Sorger (2006) to a continuous time setting. The underlying idea is that, in case of disagreement, the threat is that players will play a noncooperative Markov Perfect Nash equilibrium just during a very small period of time, since new negotiations can take place at every future moment and, in particular, immediately later. Conditions for interior TCB solutions are derived. To illustrate the results, two common property resource games are analyzed in detail.

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