Consider an individual facing the prospect of having high income, m; > 0, with probability 7:" and low income, 311,, with probability 1 7r, 3);; > 95;. Prior to learning whether realized income is high or low, the individual is able to go into the market and purchase (or sell) two types of assets. Let the Asset 1 have a return structure such that it pays R1,H units of goods if y = yH and pays R131, units of goods if y = M. Similarly, let Asset 2 have a return structure such that it pays R2,]; units of goods if y = 3m and pays RM, units of goods if y = M. The individual is endowed with to units of wealth to spend in the asset market but this wealth is not storable and hence cannot be save to purchase consumption goods. Denote by a1 the amount of Asset 1 purchased by the individual and (12 the amount of Asset 2 purchased by the individual. The individual's problem is to maximize the expected utility from consumption sub- ject to the constraints that consumption must be nanced out of income and the realized return from the asset portfolio as well as a constraint that spending on the asset portfolio must be nanced out of the non-storable endowment wealth to. Consumption and portfolio spending satises the following constraints, CH 2 21H + R1,Ha1 + R2,H612 (1) CL = 21L + Rnrl + R2,L02 (2) w = a1 + a2. (3) Note that al and (12 can be positive (purchase) or negative (sell). Denition 1 An asset structure is complete from the perspective of an economic actor if the actor is, in eect, unrestricted (up to their budget constraints) in the ability to transfer wealth across states-of-natare. One way to think about this is that if there are N statesofnature, then a complete asset structure allows the individual the exibility to construct combinations of payoffs that can vary in N different directions. If the asset structure is incomplete then the individual can only choose from payoffs that vary in M