DAT610 MOD8-1 Exercise (1)
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Industrial Engineering
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Feb 20, 2024
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8-1 EXERCISE
DAT 610
NOVEMBER 12, 2023
SNHU
Destiny Denson
Monte Carlo simulations provide a robust approach to estimate complex scenarios, exemplified in the context of determining the maximum annual "Collision" loss with 99.9% certainty. The initial step involves utilizing R to draw a random sample from a Poisson distribution, reflecting the average loss frequency. This distribution is critical as it introduces the necessary stochastic element, capturing the variability inherent in real-world situations.
1.
Import the data set and read or view it as a string.
X
Moving to the second aspect, the average loss severity is determined by calculating the mean and
standard deviation of the "Collision" loss amount from the IIHS data. These values are then transformed into parameters for a lognormal distribution, which effectively represents the uncertainty associated with loss severity. R is employed to draw a random sample from this lognormal distribution, thereby incorporating another layer of randomness into the Monte Carlo simulation.
2.
Determine the crashes per year.
The third step in the process involves multiplying the random value drawn from the Poisson distribution (representing loss frequency) by the random value drawn from the lognormal distribution (representing loss severity). This multiplication is repeated four more times, and the maximum product from these iterations is identified. This iterative process enables the Monte Carlo simulation to simulate the total loss, accounting for both frequency and severity components.
3.
Draw a Sample From a Poisson Distribution With a Mean Equal to the Average Number of Loss Events Per Year.
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4.
Determine the Average and Standard Deviation of the “Collision” Loss Amount
5.
Draw a Sample Value From a lognormal Distribution
6.
Multiply the random value drawn from the poisson distribution by the random value drawn from the lognormal distribution.
To achieve a 99.9% confidence level regarding the maximum likely annual loss to fraudulent claims, the simulation must be run numerous times. The fourth step outlines the Monte Carlo extrapolation process: running the simulation at least 1000 times. After collecting the results, sorting them in ascending order, the 1000th value is selected as the estimated maximum annual loss. This systematic approach enhances precision and reliability compared to relying solely on a limited dataset.
7.
Repeat four times.
Monte Carlo simulations find broad applications in real-world scenarios marked by complexity and uncertainty. Beyond insurance, these simulations prove valuable in financial forecasting, project management, and risk assessment. In the realm of insurance and risk modeling, Monte Carlo simulations are particularly adept at predicting extreme events, such as maximum annual losses, by considering the intricate interplay of various factors influencing the outcome. This adaptability positions Monte Carlo simulations as a powerful tool for decision-making in situations characterized by intricate uncertainties, making them invaluable in various domains.
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Citations:
Camac, K. (n.d.). Module 8 . Sign in to your account. https://learn.snhu.edu/d2l/le/news/1394272/6310028/view What is The Monte Carlo Simulation?
(1978) Amazon
. Available at: https://aws.amazon.com/what-is/monte-carlo-simulation/ (Accessed: 12 November 2023).