A Common Application of Monte Carlo Simulation Is to Provide

question 15

Essay

A common application of Monte Carlo simulation is to provide numerical approximations. One such application is to approximate the area under a curve, or Monte Carlo integration. The following figure represents such a curve, defined over the range of X = 0 to X = 13. Call the area under this curve a.Monte Carlo integration begins by overlaying on the curve of interest a region (call this region, B) whose area is easy to calculate (i.e., a box). Monte Carlo integration then involves the random generation of points in B and a determination of the percentage of these points that fall in A (i.e., fall below the curve). This percentage represents that portion of the area of B that is the area of a.Use Monte Carlo integration techniques to approximate the area under the curve. Use exact techniques to calculate the true area under the curve. How accurate is your approximation?

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Definitions:

Prospect Theory

A behavioral economic theory that describes how people choose between probabilistic alternatives that involve risk, where the probability of outcomes is known.

Marginal Disutility

The added dissatisfaction or inconvenience experienced by consuming one more unit of a good or service.

Marginal Utility

The extra utility a consumer obtains from the consumption of 1 additional unit of a good or service; equal to the change in total utility divided by the change in the quantity consumed.

Absolute Terms

A method of expression or measurement that is independent of other variables or comparisons, focusing on intrinsic values.