BA3202-L12 - BA3202 Actuarial Statistics Lecture 12 Monte...

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BA3203 L12 BA3202 Actuarial Statistics Lecture 12: - Monte Carlo Simulation
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BA3203 L12 Introduction Monte Carlo simulation: computational algorithms that rely on repeated random sampling to obtain numerical results Why? Easy to understand the basic steps High-speed PC Lack of analytical solutions Some terms used in lecture A random variate: A realization of a rv generated by a computer A random number: A random variate generated from U(0, 1) pseudo-random number generator: an algorithm for generating a sequence of numbers that approximates sequences of random numbers from U(0, 1) or N(0,1) The generated sequence is not truly random but deterministic. The best known pseudo-random generating process is called a linear congruential generator (LCG) Actuarial Science NTU Jade Nie [email protected] 2
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BA3203 L12 Generation of random variates from a specified distribution Assuming we have a sequence of random number fro U(0,1) available Main general methods: Inverse transform method Acceptance-rejection method Special methods for generating N(0,1) rv’s Box-Muller algorithm Polar algorithm Actuarial Science NTU Jade Nie [email protected] 3
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BA3203 L12 Inverse transform method Recall for any rv 𝑋 with cdf 𝐹 𝑥 𝑦 = 𝐹 𝑥 is a strictly increasing function from 0 to 1 Taking the inverse of the cdf, we have 𝐹 −1 𝑦 = 𝑥 is the inverse function to 𝐹 𝑥 If a random variable 𝑈 ~ 𝑈 (0,1)
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