Financial/Actuarial Mathematics Seminar

Thursdays 3:10-4:00, 3088 East Hall



Pareto Optimal Risk Allocations

Virginia (Jenny) Young

Department of Mathematics, University of Michigan

February 1, 2007



Abstract

In this talk, I will describe work in progress with S. David Promislow (York University). The basic problem is as follows: Given $n$ agents, each of whom faces a random loss and each of whom seeks to minimize their risk according to some risk measure, find a Pareto optimal allocation of the total loss. That is, find an allocation such that no agent can made happier without making at least one other agent less happy. I will show that under a mild condition for the risk measures, Pareto optimal allocations can be expressed as a collection of $n$ non-decreasing functions of the total random loss. I will also discuss how the problem of finding Pareto optimal allocations is related to finding minimal points of convex sets in $R^n$, under the partial coordinate-wise ordering. In particular, I will give some interesting results for $R^2$.


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