CS计算机代考程序代写 finance Assignment 3

Assignment 3
Microeconomics for MFE, UofT

Due by the end of Wednesday, December 3rd

This problem is roughly based on DeMarzo, Peter, and Yuliy Sannikov “Op-
timal Security Design and Dynamic Capital Structure in a Continuous-Time
Agency Model,” The Journal of Finance (2007).

In this problem, you are required to implement DeMarzo-Sannikov model
and do comparative statics. Consider the following baseline parameters: L = 25,
R = 0, µ = 10, σ = 5, r = .1, γ = .15, λ = 1, K = 30.

1. Find the principal’s value function P (W ). Recall that P (W ) is given by

µ+ γWP ′(W ) + 1
2
λ2σ2P ′′(W ) = rP (W )

on W ∈ [R, W̄ ] with boundary conditions P (R) = L, P ′(W̄ ) = −1, and
γW̄ + rP (W̄ ) = µ. One way to solve this equation is by :

(a) constructing a grid of slopes α = P ′(R), and solving first the differ-
ential equation with initial conditions P (R) = L and P ′(R) = α;

(b) then, for each α, you can find W̄ (α) from γW̄ (α) + rP (W̄ (α)) = µ;
(Hint: this is not necessarily solvable for every value of α.)

(c) finally, you can determine α for which P ′(W (α)) = −1.

2. The model has the following parameters: L, R, γ, µ, λ. Pick any two
parameters p1 and p2. Describe what happens to the firm’s debt D =
1
r

(
µ− γ

λ

)
and its credit limit CL = (W̄ − R)/λ as you vary each one

of the two parameters. Does the effect always go in the same directions?
Provide intuition for your results.

1