maria lives 2 periods. in period 1, she is a student, her income is 0 and she do

Question

maria lives 2 periods. in period 1, she is a student, her income is 0 and she does not pay axes. in period 2, she will have a BA. her income after tax will be $55000. the interest rate is 10%, her utility is given by U(c, c')=log(c)+log(c'). It can be shown that the optimal consumption allocation is c=05we, c'=0.5(1+r)we

1. determine Maria's lifetime wealth.

2. Determine comsumption and savings of Maria in period 1 and in period 2.'

3. Maria decides to switch a major and is now a student in business. in period 2, she will have a BA in business and her income will be $88000. determine Maria's lifetime wealth. determine consumption and sacving of maria in period 1 and period 2.

Explanation / Answer

We consider a consumption-portfolio problem in continuous time under uncertainty. A martingale technique is employed to characterize optimal consumption-portfolio policies when there exist nonnegativity constraints on consumption and on final wealth. We also provide a way to compute and verify optimal policies. Our verification theorem for optimal policies involves a linear partial differential equation, unlike the nonlinear partial differential equation of dynamic programming. The relationship between our approach and dynamic programming is discussed. We demonstrate our technique by explicitly computing optimal policies in a series of examples. In particular, we solve the optimal consumption-portfolio problem for hyperbolic absolute risk aversion utility functions when the asset prices follow a geometric Brownian motion. The optimal policies in this case are no longer linear when nonnegativity constraints on consumption and on final wealth are included. By these examples, one can see that our approach is much easier than the dynamic programming approach. A general consumption/investment problem is considered for an agent whose actions cannot affect the market prices, and who strives to maximize total expected discounted utility of both consumption and terminal wealth. Under very general conditions on the nature of the market model and on the utility functions of the agent, it is shown how to approach the above problem by considering separately the two more elementary ones of maximizing utility of consumption only and of maximizing utility of terminal wealth only, and then appropriately composing them. The optimal consumption and wealth processes are obtained quite explicitly. In the case of a market model with constant coefficients, the optimal portfolio and consumption rules are derived very explicitly in feedback form (on the current level of wealth). and for part 2 refer below link Read More: http://epubs.siam.org/doi/abs/10.1137/0325086 http://www.thelyongroup.net/Lifetime-Wealth-Portfolios.5.htm http://www.free-online-calculator-use.com/earnings-calculator.html

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