30E00400 - Simulation D, Lecture, 5.9.2022-20.10.2022

Topic outline

• Materials
  • Select activity Lecture 2

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    Review of probability and statistics, Randomness in Excel
    

    Recommended readings:
    

    Ross: Chapter2; 2.1.-2.7, 2.8 (binomial distribution), 2.9 (normal distribution), 2.10 (4th ed.)

    Evans and Olson:  Chapter 3: p. 63-77 (2nd ed.)

    Lecture slides are attached.

  • Select activity Lecture 3

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    Illustration of Sampling distribution and Central Limit Theorem:
    

    • https://onlinestatbook.com/stat_sim/sampling_dist/
      

    Probability calculations (Test accuracy, Bayes rule)
    Simulation from discrete probability distributions (table form): investment example
    Inverse function method in simulation
    
    Recommended readings:
    Ross: Chapter 4.1, p. 49-50; Chapter 5.1, p. 67-71 (in 4th ed.)
    Evans and Olson: Chapter 2, Chapter 3, p. 81-88, 93-97 (in 2nd ed.)
    
    
    
    
  • Select activity Lecture 4

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    Theory of Random Numbers
    

    Waiting time distributions

    Recommended readings:

    Ross:  Chapter 3, p.41-48; Ch. 2.8, p-22-23, Ch. 2.9, p. 27-29, Ch. 4, example 4d, p. 53-54  (in 4th ed.)

    
    

    
    

  • Select activity Lecture 5

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    Special Methods: Composition Method and Acceptance/Rejectance Method
    

    (See also lecture 4)
    

    Recommended readings:
    

    Composition method: Ross, Ch. 4.5,p. 60-61 in 4th ed. (in the book composition method is explained for discrete RV's, in class for continuous RV's), 

    Acceptance-Rejection Method: Ross, Ch. 4.4, p. 58-60  (discrete RV), Ch. 5.2. p. 71-78, (continuous RV); in 4th ed.. The procedure is explained in an alternative way compared to lectures. 

  • Select activity Lecture 8

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    Random vectors

    Cholesky decomposition

    Simulation of multivariate normal distribution

    Material on Multivariate normal and other distributions
    Recommended readings: https://en.wikipedia.org/wiki/Multivariate_normal_distribution
    Further readings on random vector and multinormal distribution (Advanced): https://www.webpages.uidaho.edu/~stevel/519/Applied%20Multivariate%20Statistical%20Analysis%20by%20Johnson%20and%20Wichern.pdf
    

  • Select activity Lecture 10

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    System simulation: Theory and examples
    

    Readings:

    Evans and Olson, Ch. 6, p. 199-245 (2nd. ed) ; attached partially

    Ross, Ch. 6-1.-6.5, p. 93-103 (4th. ed.)
  • Select activity Lecture 11

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    System Simulation: Examples (see also lecture 10)

    Poisson process
    

      Recommended Readings: Ross: Ch. 2., p. 20-22 and 29-33; Ch. 5.4-5.5., p. 82-87. 

    Stochastic Processes: Random Walk Models
    

      Readings (Option value): Ross, p. 198-199 (4th ed.)

    
    

  • Select activity Lecture 12

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    Simulation of stock price
    

    Review. Exam Issues, Questions?
    

    
    

  • Select activity Lecture 6

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  • Select activity Lecture 7, 2022

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    Simulation from Normal distribution and some other distributions

    Recommended readings:

    Ross (as shown in 4th ed.): Ch.5.3. p.78-80,

    Evans and Olson (as in 2nd ed,): Ch.3. p. 71-88.

    
    

  • Select activity Lecture 9, 2022

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    Lecture 9, 2022 Folder