772 JAN MOSSIN (utility function) of the form: over all possible portfolios, 1. e,, we postulate that an individual will behave as if he were attempting to maximize U. with respect to the form of Ui, we shall assume that it is concave, with the first derivative positive and the second negative. This latter assumption of general risk aversion seems to be generally accepted in the literature on portfolio selection. The investor is constrained, however, to the points that satisfy his budget equation ∑p/(x-动)+q(x-x)=0, old "portfolio should equal total outlays on the"new"portfolio Formally, then, we postulate that each individual i behaves as if attempting to maximize(3), subject to(4),(1), and (2). Forming the Lagrangean v=f(y,y)+0∑1(x-动)+8(x we can then write the first-order conditions for the maxima for all i as ax=+2f1x+时p=0 〔=1,…,n-1) f+0 n-1 ∑p(对-对)+(x一x where fi and fi denote partial derivatives with respect to yi and y2, respectively Eliminating 8 this can be written as 两-p/ 1), 点2 In(5), the-filIfi is the marginal rate of substitution dy2/dyi between the variance has content downl ued stube to sT oR ems aecondtp23013020-0 AM772 JAN MOSSIN (utility function) of the form: (3) U =PA(Y, YD) over all possible portfolios, i.e., we postulate that an individual will behave as if he were attempting to maximize Ui. With respect to the form of Ui, we shall assume that it is concave, with the first derivative positive and the second negative. This latter assumption of general risk aversion seems to be generally accepted in the literature on portfolio selection. The investor is constrained, however, to the points that satisfy his budget equation: n-i (4) EPij(XJ-XJ) +q(xn-5n) = ? s where XJ are the quantities of asset j that he brings to the market; these are given data. The budget equation simply states that his total receipts from the sale of the "old" portfolio should equal total outlays on the "new" portfolio. Formally, then, we postulate that each individual i behaves as if attempting to maximize (3), subject to (4), (1), and (2). Forming the Lagrangean: VZ=fJ(4Y, y2)+0 ' Pi i)+g(Xn- K) we can then write the first-order conditions for the maxima for all i as: avi n-1 av f4 +2fP Eoje4+O pj=o (j=1, ..., n-1), = f'+Olq=O, avi n-1 -=E pj (Xj-Xj)~ + q(x - 5in) = O wherefl' and f2i denote partial derivatives with respect to y' and y', respectively. Eliminating 0', this can be written as: i2Eafja Xx (5) _=a, n-1), f2 1ju-pj/q n-i (6) E Pj (XJ-Xj) + q(xn-Xn')= j=t In (5), the -f;i/f2' is the marginal rate of substitution dyi ldy' between the variance This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:20:50 AM All use subject to JSTOR Terms and Conditions