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

Prove that its inclination is given by cot = b cot - a, Two stations due...

Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot.  If α ,  β be the elevations of the top of the tower from these

How to solving one-step equations, How to Solving One-Step Equations? E...

How to Solving One-Step Equations? Equations, where one math operation is acting on the variable, can be solved in one step. The trick is to get the variable x by itself - isol

In an election contested between a and b determine vote, In an election con...

In an election contested between A and B, A obtained votes equal to twice the no. of persons on the electoral roll who did not cast their votes & this later number was equal to twi

Evaluate the linear equation, Evaluate the linear equation: Solve the ...

Evaluate the linear equation: Solve the equation ax - b = c for x in terms of a, b, and c. Solution: Step 1. Using Axiom 1, add b to both sides of the equation. a

Linear Equations, y= -3x tell if it is linear or not. our teacher wants it ...

y= -3x tell if it is linear or not. our teacher wants it graphed or something.

Sequence-or-series, in and ap 1,2,3,4,5,6,7,8,9 11,12,13,14,15,16,17,18,19...

in and ap 1,2,3,4,5,6,7,8,9 11,12,13,14,15,16,17,18,19 and like that nonzzero digit find tn Solution) First break the ''n'' number in terms of 10''s power. For e.g if n=3259 wri

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