The Asset Pricing Model With General Deviation Measure Of The Coalition

In the last ten years, the theory of optimal risk sharing is played more and more attention. Especially, how the interaction of the agency with its own risk preference is a important subject. These problems usually show in the following form:given a random revenue X and m investors, we need to find a allocation plan of X, which is （Y₁, Y₂,…,Y_m）, and such that this plan is allowed for all investors, where Yj is the gain of the j investor.By defining the coalition deviation to measure the overall risk of the coalition, Rockafellar, Uryasev and Zabarankin give an allocation on expected earnings and they turn out this program is in the core of a cooperative game. Therefore, using a given "fair" plan to allocate expected revenue coalition, each investor’s utility have been improved. However, based on rational assumptions, all investments in the market who will constitute the alliance to cooperate. At this time whether the market no arbitrage, and how to price for assets, become the primary problem, this paper will explore the conditions for the arbitrage-free market and gives specific expression for assets pricing.First of all, based on optimization theory subgradient and convex analysis, we demonstrate that there is the optimal portfolio in a deviation measures of the coalition. Then, from the perspective of a balanced distribution alliance, we give the definition and form of the alliance equilibrium pricing function. By observing equilibrium pricing function form and combined with the Riesz representation theorem, we find that the random variable L is possible to become a Radon-Nikodym derivative. At this point, we can analyze the characteristic of investors and portfolio in different point. First, from the view of the strategy stability, the generalized Sharpe ratio is the intrinsic nature of a strategy, and it describes that a portfolio can bring how many units excess returns in per unit of risk. In addition, from the point of view of investors risk structure, the lower range dominance is the inherent nature of the investors, and it is used to describe the prefer of investor in risk. Finally, we show that, when generalized Sharpe ratio less than 1, and investors’deviations are the lower range dominance, there is martingale measure P which is equivalent to probability measure P. That is, we prove that the market at this time is no arbitrage.This paper is divided into four chapters:The first chapter briefly introduces the concept of optimal risk sharing theory, generalized deviation measure significance in the optimal portfolio analysis and generalized deviation measure in risk analysis research background. The second chapter, first shows preference relations and introduces the Utility Theorem Then introduces the basic concepts of cooperative game and give some practical common method of risk measurement. Finally, the convex analysis theory will also be showed. The third chapter we will find the optimal portfolio in a deviation measures of the coalition. The fourth chapter,first we will find the formula of the pricing function, and then proves it is risk-neutral. In final, we show an example when the general deviation measures of the coalition is a standard lower semideviations.