Finally, consider the asset return structure (R1,L, R1,H) and (R2,L, R2,H) with R1,HxR2.H and R1.L =vectors lie on top of either of the axes. Show that sums of asset combinationscan reach any point in the (RL, RH)-plane. What does this mean? Note that ourassumption implies that the returns to both of these assets are non-contingent.zR2.L, x 7 z. Specifically, assume that neither of the two return Consider an individual facing the prospect of having high income, YH > 0, withprobability 7 and low income, YL, with probability 1 – T, YH > YL. Prior to learningwhether realized income is high or low, the individual is able to go into the market andpurchase (or sell) two types of assets. Let the Asset 1 have a return structure such thatit pays R1.H units of goods if y = YH and pays R1,L units of goods if y = YL. Similarly,let Asset 2 have a return structure such that it pays R2.H units of goods if y = YH andpays R2,L units of goods if yto spend in the asset market but this wealth is not storable and hence cannot be saveto purchase consumption goods. Denote by a1 the amount of Asset 1 purchased by theindividual and az 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 financed out of income and the realizedreturn from the asset portfolio as well as a constraint that spending on the asset portfolio= YL. The individual is endowed with w units of wealthmust be financed out of the non-storable endowment wealth w.Consumption and portfolio spending satisfies the following constraints,Ун + Ri,нај + Rz, H@2YL + R1,La1 + R2,La2(1)(2)(3)CHCLai + a2.Note that aj and az can be positive (purchase) or negative (sell).

In the given scenario, we have an individual who faces the possibility of receiving either high…

Consider an individual facing the prospect of having high income, yí > 0, with probability and low income, yl, with probability 1 T, YH > YL. 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, units of goods if y = yн and pays R₁,L units of goods if y = yL. Similarly, let Asset 2 have a return structure such that it pays R₂,H units of goods if y pays R₂,L units of goods if y = yL. The individual is endowed with w 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 a2 the amount of Asset 2 purchased by the individual. Ун and The individual's problem is to maximize the expected utility from consumption sub- ject to the constraints that consumption must be financed out of income and the realized return from the asset portfolio as well as a constraint that spending on the asset portfolio must be financed out of the non-storable endowment wealth w. Consumption and portfolio spending satisfies the following constraints, Yн + R₁,Hа₁ + R₂,на₂ YL + R₁, La₁ + R₂,La2 a₁ + a₂. Note that a₁ and a2 can be positive (purchase) or negative (sell). CH = CL = = (1) (2) (3)

1st Edition

ISBN:9781285187273

Author:Camm, Jeff.

Publisher:Camm, Jeff.

Chapter11: Monte Carlo Simulation

Section: Chapter Questions

Problem 2P