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

Objectives of ones tens and more, Objectives After studying this unit, ...

Objectives After studying this unit, you should be able to 1.  evolve and use alternative activities to clarify the learner's conceptual 2.  understanding of ones/tens/hu

Objective functions, For schedule consistency, you decide to require each o...

For schedule consistency, you decide to require each officer to report for their eight-hour shift at 12 AM, 4 AM, 8 AM, 12 PM, 4 PM, or 8 PM. As the Director of Public Safety, you

Determine the measure of a base angle, The angle calculate of the base angl...

The angle calculate of the base angles of an isosceles triangle are shown by x and the vertex angle is 3x + 10. Determine the measure of a base angle. a. 112° b. 42.5° c.

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Understand the terms quotient and remainder, What other activities can you ...

What other activities can you suggest to help a child understand the terms 'quotient' and 'remainder'? Once children understand the concept and process of division, with enough

Equivelent ratios, if 2 ballons cost 12 coins,use equivelent ratios to see ...

if 2 ballons cost 12 coins,use equivelent ratios to see how many coins 8 ballons would cost

Exponential functions, The exponential functions are useful for descr...

The exponential functions are useful for describing compound interest and growth. The exponential function is defined as:          y = m. a x where '

Calculate the acceleration time, Question A 22 kW, 3-phase, 415 V, 40 A,...

Question A 22 kW, 3-phase, 415 V, 40 A, 50 Hz, 960 rpm, 0.88 PF squirrel cage induction motor drives a pump. The total inertia of the drives system is 1.2 kg-m2. Determine th

The achievements from math, i love math..but i am afraid to study it... i m...

i love math..but i am afraid to study it... i mean i ma afraid that it may leave me in clay...what can you suggest me?

Geometry, in right angle triangle BAC.

in right angle triangle BAC.

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