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

Chanllenge, a pizza driver delivered 27 pizzas in one night he delivered mo...

a pizza driver delivered 27 pizzas in one night he delivered more then one pizza to only one house . every other house he only delivered pizza to 18 houses . how many pizzas did he

Areas of a rectangle, a rectangular field with a path around it measures 1...

a rectangular field with a path around it measures 120m by 50m.if the path is 1m wide all around,(a)find the length of the outer edge of the path.(b)find the area of the path

Math, what is 24566x12567=

what is 24566x12567=

Calculate percentage of increasing customer, Coastal Cable had 1,440,000 cu...

Coastal Cable had 1,440,000 customers within January of 2002. During the first half of 2002 the company launched a large advertising campaign. Through the end of 2002 they had 1,80

Children have their own strategies for learning maths, Children Have Their ...

Children Have Their Own Strategies For Learning Vibhor, aged 7, was once asked if he knew what 'seven lots of eight' are. He said he didn't. He was then asked, "Can you work it

The stoichiometric reaction, Prove that a reaction following the rate law v...

Prove that a reaction following the rate law v = k[A] 2 is characterized by a linear plot of [P] t 1 versus t-l, where P is the product of the stoichiometric reaction A = P. Sho

Ratio test - sequences and series, Ratio Test In this part we are goin...

Ratio Test In this part we are going to take a look at a test that we can make use to see if a series is absolutely convergent or not.  Remind that if a series is absolutely c

Krystal, what is the tenths place

what is the tenths place

Briefly explain markov chains, Question 1 An experiment succeeds twice as ...

Question 1 An experiment succeeds twice as often as it fails. Find the chance that in the next six trials there will be at least four successes Question 2 An insurance compan

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