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lec0203 - IEOR 4106 Professor Whitt Lecture Notes Thursday...

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IEOR 4106: Professor Whitt Lecture Notes, Thursday, February 3 Even More on Markov Chains Examples 1. A Markov Chain Example in Credit Risk Modeling See the separate handout, also posted on the web page. 2. Examples 4.1 and 4.4: weather forecasting. 3. Example 4.7: automobile insurance premiums. This is the insurance example, Example 4.7 in the textbook. This is a slight simpli- fication of a realistic application of Markov chains. We construct the model by constructing the transition matrix, given in the book: P = a 0 a 1 a 2 1 - a 0 - a 1 - a 2 a 0 0 . 0 a 1 1 - a 0 - a 1 0 . 0 a 0 0 . 0 1 - a 0 0 . 0 0 . 0 a 0 1 - a 0 There are four states: 1 , 2 , 3 , 4, with state 1 being the bonus (good) state. Higher states mean a worse claim record, but in this case we place an upper limit of 4. The elements of the 4 × 4 matrix are probabilities: a k is the probability of having k accidents (actually making k claims) during the year. The row sums necessarily are 1. The probability entries a k here are in this case in the book are computed as Poisson probabilities; i.e., then a k = e - λ λ k k !
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