economics, Mathematics

Assignment Help:
A mortgage lender seeks to maximize the expected value of its portfolio. The portfolio, of course, is the
sum of all of the mortgages in it, so no generality is lost by examining the case of one loan:
E[port] = (1-p).B +p.(V-L)
where:
_ E[port] is the expected value of the portfolio
_ p is the probability of foreclosure
_ B is the principal balance
_ V is the sale price at foreclosure
_ L is the legal fees incurred by foreclosure
Assume that the borrower’s probability of foreclosure is an increasing function of his/her ”balance-to value ratio” (i.e. B/V):
P ? p (B/V) P’>0
In other words, borrowers who are deeper underwater are more likely to enter the foreclosure process. In such cases, reducing principal balances would reduce foreclosure-related losses (by reducing the probability of foreclosure). On the other hand, principal balance reductions are a direct loss for the lender.
1. Derive the marginal benefit of reducing principal balances.
2. Derive the marginal cost of reducing principal balances.
3. What is the necessary condition for maximizing E[port] with respect to the principal balance?
4. What is the sufficient condition for maximizing E[port]?
5. How does the marginal benefit curve shift in response to an increase in L?
6. How does the marginal cost curve shift in response to an increase in L?
7. How does the optimal principal balance change when L increases?

Related Discussions:- economics

Confidence interval, Confidence Interval The interval estimate or a 'co...

Confidence Interval The interval estimate or a 'confidence interval' consists of a range as an upper confidence limit and lower confidence limit whether we are confident that a

Geometry, #question.prove that the diagonals of a trapezium divide each oth...

#question.prove that the diagonals of a trapezium divide each other proportionally .

Determine the volume of the object, A rectangular container is 15 cm wide a...

A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the

Prove that op=2ap, Two tangents PA and PB are drawn to the circle with cent...

Two tangents PA and PB are drawn to the circle with center O, such that ∠APB=120 o . Prove that OP=2AP. Ans:    Given : - ∠APB = 120o Construction : -Join OP To prove : -

Example of parametric equations and parametric curves, Draw the parametric ...

Draw the parametric curve for the subsequent set of parametric equations. X = t 2 +t Y=2t-1 -1 t 1 Solution Note that the only dissimilarity here is the exis

Nemeric patterns, Kelli calls her grandmother every month. Every other mont...

Kelli calls her grandmother every month. Every other month,Kelli also calls her cousin in January, how many calls will Kelli have made to her grandmother and her cousin by the end

In how many years is the population expected to be 42, The population of a ...

The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke 0.1t where k is a constant and t is the time in years.

5th grade math, jack and his mother paid $11.50 for tickets to the movies. ...

jack and his mother paid $11.50 for tickets to the movies. An adult''s ticket costs $4.50 more than a child''s ticket. What was the cost of each ticket?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd