Multivariate Optimized Certainty Equivalents And Risk Allocation

This paper is base on a class of monetary risk measure:Optimized Certainty Equivalents and the Multivariate monetary risk measure to generalize the Opti-mized Certainty Equivalents to Multivariate case,that is,Multivariate Optimized Certainty Equivalents(MOCE),and make sure that it is a class of multivariate monetary risk measure.Also we want to determine the risk allocation afterward-s.Firstly,we rewrite the theory of Optimized Certainty Equivalents in "loss"case and provide the proof of the theorem of the existence and uniqueness of the optimal allocation.Secondly,we give two different definition of the Multivariate Optimized Certainty Equivalents,they are MOCE(?)and MOCE(?)respective-ly.In the first case,MOCE has the directly economic meanings.We study the properties of the MOCE(?)and prove the theorem of the existence and unique-ness of the optimal allocation in this case,and provide the way to determine the risk allocation.In the second case,MOCE(?)can show the relation between different risk factors in the financial system by using the loss function.This part we study deeply,we also study the properties of the MOCE(?)and prove the theorem of the existence and uniqueness of the optimal allocation in this case,see Theorem 4.4.Then we provide the way to determine the risk allocation also.In the thesis,we provide many examples to introduce the way to calculate the optimal allocation and the MOCE.We show the relation between the the MOCE value and the parameter systemic risk weight a and the correlation r between the risk factors.Lastly we use Monte Carlo method give a sound way to calculate the optimal allocation such that save a lot of computation time,which gives an opportunity for the application of the MOCE in the industry.