设 U(x) 为utility function（效用函数）x为wealth level. 在这两篇论文中（Portfolio insurance and volatility regime switching, Joel M Vanden) (Asset Prices and Alternative
Characterizations of the Pricing Kernel,  Erik Lüders) 都写有
It is well known that in the equilibrium of a representative investor economy the following equality must hold
             dU/dx=\lambda * \xi(T)
这里\lambda is a constant to be determined in equilibrium, \xi(T)是pricing kernel.
请问这个式子是怎么得到的？

另外，这两篇文章在这个问题上都给出了以下三个reference：
1。Cox, J.C. and Huang, C. (1989). Optimal Consumtion and Portfolio
Policies when Asset Prices Follow a Diffusion Process, Journal of Economic
Theory, 49, 33-83.
2。Cox, J.C. and Huang, C. (1991). A variational problem arising in financial
economics, Journal of Mathematical Economics, 20, 465-487.
3。Karatzas, I.; Lehoczky, J. P. and Shreve, S. E. (1987). Optimal Portfolio
and Consumption Decisions for a Small Investor on a Finite Horizon.
SIAM J. Control and Optimization, 25, 1157-1586.