Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 % , then $ 1000 worth of purchasing power now will have only $ 970 worth of purchasing power in 1 year because 3 % of the original $ 1000 ( 0.03 × 1000 = 30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that $ P will purchase after n years is A = P · ( 1 − r ) n where r is expressed as a decimal. Inflation If the average inflation rate is 2 % , how long is it until purchasing power is cut in half?
Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 % , then $ 1000 worth of purchasing power now will have only $ 970 worth of purchasing power in 1 year because 3 % of the original $ 1000 ( 0.03 × 1000 = 30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that $ P will purchase after n years is A = P · ( 1 − r ) n where r is expressed as a decimal. Inflation If the average inflation rate is 2 % , how long is it until purchasing power is cut in half?
Solution Summary: The author explains that inflation is a term used to describe the erosion of the purchasing power of money.
Inflation
Problems 57-62 require the following discussion.
Inflation
is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is
, then
worth of purchasing power now will have only
worth of purchasing power in 1 year because
of the original
has been eroded due to inflation. In general, if the rate of inflation averages
per annum over
years, the amount
that
will purchase after
years is
where
is expressed as a decimal.
Inflation
If the average inflation rate is
, how long is it until purchasing power is cut in half?
The OU process studied in the previous problem is a common model for interest rates.
Another common model is the CIR model, which solves the SDE:
dX₁ = (a = X₁) dt + σ √X+dWt,
-
under the condition Xoxo. We cannot solve this SDE explicitly.
=
(a) Use the Brownian trajectory simulated in part (a) of Problem 1, and the Euler
scheme to simulate a trajectory of the CIR process. On a graph, represent both the
trajectory of the OU process and the trajectory of the CIR process for the same
Brownian path.
(b) Repeat the simulation of the CIR process above M times (M large), for a large
value of T, and use the result to estimate the long-term expectation and variance
of the CIR process. How do they compare to the ones of the OU process?
Numerical application: T = 10, N = 500, a = 0.04, x0 = 0.05, σ = 0.01, M = 1000.
1
(c) If you use larger values than above for the parameters, such as the ones in Problem
1, you may encounter errors when implementing the Euler scheme for CIR. Explain
why.
#8 (a) Find the equation of the tangent line to y = √x+3 at x=6
(b) Find the differential dy at y = √x +3 and evaluate it for x=6 and dx = 0.3
Q.2 Q.4 Determine ffx dA where R is upper half of the circle shown below.
x²+y2=1
(1,0)
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