Hi there for the question in September-2017 Q1ii, can I ask how we calculate out the integration of CDF out ? Thanks in advance.
You don't. Integration of CDF is for the continuous case only. To find first order stochastic dominance in the discrete case, you are finding probability that the return is less or equal to the given value, so that it becomes {0.2, 0.4, 0.6, 0.8, 1.0} for Asset 1 {0.3, 0.5, 0.6, 0.8, 1.0} for Asset 2 {0.1, 0.4, 0.6, 0.9, 1.0} for Asset 3 If you had to sketch the F(x) graph out, it will be in step functions. Same for its integral. Second order stochastic dominance is determined by sum of cumulative probabilities, so you must use the set of values given above (even if not explicitly asked for the first set of values), so that it becomes {0.2, 0.6, 1.2, 2.0, 3.0} for Asset 1 {0.3, 0.8, 1.4, 2.2, 3.2} for Asset 2 {0.1, 0.5, 1.1, 2.0, 3.0} for Asset 3 Then you use the argument how sum of cumulative probabilities for Asset 3 at any point is less than or equal to that of Asset 1, and hence it exhibits second-order stochastic dominance. Similar logic applies to the other two pairs.
