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)
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)
Essentials Of Business Analytics
1st Edition
ISBN:9781285187273
Author:Camm, Jeff.
Publisher:Camm, Jeff.
Chapter11: Monte Carlo Simulation
Section: Chapter Questions
Problem 2P
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