 ## Math 490 (Stochastic Processes for Finance and Insurance)

• Test 1
Test 2
Test 3

• Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8
Homework 9
Homework 10
Homework 11

• Test 1
Test 2
Test 3
• ### Class Diary

• Wedensday, 01/17: sample spaces and events, probabilities, conditional probabilities, independence
• Friday, 01/19: Bayes' formula, random variables, discrete random variables, (absolutely) continuous random variables
• Monday, 01/22: expectation of a random variable, expectation of a function of a random variable, variance of a random variable
• Wedensday, 01/24: joint distributions, marginal distributions, joint mass functions, marginal mass functions, joint densities, marginal densities, covariances
• Friday, 01/26: distributions of sums of independenr random variables, momemnt generating functions, laws of large numbers, central limit theorems
• Monday, 01/29: stochastis processes, conditional mass functions, conditional density functions, condistional expectations
• Wedensday, 01/31: computing expectations by conditioning, computing variances by conditioning
• Friday, 02/02:computing probabilities by conditioning
• Monday, 02/05:compound random variable identity
• Wedensday, 02/07:Markov chains, transition probabilities, n-step transition probabilities, Chapman-Kolmogorov equations
• Friday, 02/09:Chapman-Kolmogorov equations, n-step transition probabilities
• Monday, 02/12: n-step transition probabilities (continued)
• Wedensday, 02/14:classification of states
• Friday, 02/16:recurrence, transience, random walks.
• Monday, 02/19:long-run proportions and limiting probabilities
• Wedensday, 02/21:stationary distributions. Review
• Friday, 02/23: Test 1 will cover materials up to (including) Section 4.3. Test 1: score distribution (out of 80 points): 80 2 79 1 76 1 75 2 74 1 73 1 69 1 66 1 65 1 61 1 60 1 57 1 55 2
• Monday, 02/26: Gambler's ruin, mean time spent in transient states
• Wedensday, 02/28:branching processes
• Friday, 03/02:branching processes (continued), time reversible Markov chains
• Monday, 03/05: time reversible Markov chains (continued), exponential distributions
• Wedensday, 03/07:properties of exponential random variables, failure rates, hyperexponential random variables
• Friday, 03/09:hypoexpential random variables, Coxian random variables, counting processes
• Monday, 03/12:Poisson processes, interarrival times, waiting time until the nth event
• Wedensday, 03/14:further properties of Poisson processes conditional distribution of arrival times.
• Friday, 03/16: nonhomogeneous Poisson processes, compound Poisson processes
• Moday, 03/26: Continuous-time Markov chains, birth and death processes
• Wedensday, 03/28: Review for Test 2, birth and death processes
• Friday, 03/30: Test 2: Materials on Test 2 include all Chapter 4, and Section 5.2 and 5.3. Score distributions: 80 2 76 1 75 3 72 1 70 2 65 2 64 1 58 1
• Monday, 04/02: Transition probabilities, Example 6.8, expected time for a birth and death process to go from a state i to a state j>i
• Wedensday, 04/04:variance of the time for a birth and death process to go from a state i to a state j>i, Lemmas 6.2 and 6.3
• Friday, 04/06: backward equations and forward equations
• Monday, 04/09: limiting probabilities
• Wedensday, 04/11:limiting probabilities
• Friday, 04/13: structure functions, minimal paths, minimal path sets
• Monday, 04/16:minimal cut, minimal cut sets, reliability function, systems with independent components