Optimal Risk Sharing And Trade Of Comonotonic Subadditive Risk Measures

In the research of risk theory and practical application in financial market,more and more scholars pay attention to the optimal allocation of risk and financial decisionmaking.Based on the theory of nonlinear expectation theory,this paper studies the properties of Pareto optimal allocation,the characterization of some important conclusions about the existence conditions of agreeable trades and bets under a special kind of the comonotonic subadditive risk measures(maxmin Choquet expected utility)model.Chapter 1 introduces the research background,status,main results and some preliminaries of this paper.Chapter 2 obtains some characterizations of Pareto optimal allocation under the maxmin Choquet expected utility model.Firstly,we demonstrate that all risk averse agents have a common convex capacity with the total endowment is constant,then any full insurance allocation is Pareto optimal allocation(Theorem 2.1);Secondly,we obtain the characterization of Pareto optimal allocation set(Theorem 2.3).The main results of chapter 2 enrich the conclusions of the maxmin expected utility model of Billot-Chateauneuf-Gilboa-Tallon(2000),Rigotti-Shannon-Strzalecki(2008)and Tian-Tian(2014).Chapter 3 studies the agreeable trades and agreeable bets under the maxmin Choquet expected utility model.For two risk neutral agents,we give a sufficient and necessary condition of no agreeable bets(Theorem 3.1).Then we give a sufficient condition that there is no agreeable trades(Theorem 3.2).Moreover,we discuss some characterizations of the existence of agreeable trades and bets in ex-ante and interim stages under the conditional maxmin Choquet expected utility model(Theorem 3.3 and Theorem3.4).The main results of this chapter generalize some classic characterizations of the existence of agreeable trades and bets under the conclusions of maxmin expected utility model in Kajii-Ui(2006)and Choquet expected utility model in Dominiak-EichbergerLefort(2012).Chapter 4 summarizes the main results of this paper.