An investor with initial wealth equal to one can invest in a risk-free asset with return R0, or in a risky security whose return is R1<R 0 with probability 1/2 or R2>R 0 with probability 1/2. The investor has a strictly concave vNM utility function u defined on the whole real line, such that limx→+∞u‘(x) > 0 and limx→−∞u’(x) < +∞. There are no limits on short sales. Show that the investor’s problem has a solution if and only if: limx→+∞u’(x)/ limx→−∞u'(x) < R2−R0/R0 −R1 < limx→−∞u‘(x) /limx→+∞u’(x) .


实在是没有头绪，所以想求助高手

professor之前说可以用if there is no arbitrage, a solution to the consumption-portfolio problem exists 证明