## ASRM 409 (Stochastic Processes for Finance and Insurance)

• Chap. 1
Chap. 2
Chap. 3
Chap. 4
Chap. 5
• ### Homework Assignments and Solutions

• Homework 1 for Unders Homework 1 for Grads Due 02/06
Soluton to Homework 1 for unders Solution to Homework 1 for Grads
Homework 2 for Unders Homework 2 for Grads Due 02/20
Solution to Homework 2 for unders Solution to Homework 2 for grads
Homework 3 for Unders Homework 3 for Grads Due 02/27
Solution to Homework 3 for Unders Solution to Homework 3 for grads
Homework 4 for Unders Homework 4 for Grads Due 04/02
Solution to Homework 4 for Unders Solution to Homework 4 for grads
Homework 5 for Unders Homework 5 for Grads Due 04/16
Solution to Homework 5 for Unders Solution to Homework 5 for grads
Homework 6 for Unders Homework 6 for Grads Due 05/04
Solution to Homework 6 for Unders Solution to Homework 6 for grads
• ### Tests

• Solutions for Test 1 for Unders
Solutions for Test 1 for Grads
Test 2 for Unders Test 2 for Grads
Solutions for Test 2 for Unders
Solutions for Test 2 for Grads
Final for Unders Final for Grads
• ### Class Diary

• Tuesday, 01/21: stochastic process: index set, state space, sample path, discrete-time process, continuous-time process, random walk, Markov chain chain, Poisson process, Brownian motion, geometric Brownian motion, conditioanl probability, conditional mass function
Read: Chapter 1 and 2.1.1, 2.1.2.
• Thursday, 01/23: conditional mass function, conditional density, conditional expectation, law of total expectation
Read: 2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.1.5, 2.2.1
• Tuesday, 01/28: law of total expectation, law of total variance, law of total probability, compound random variables, compounding distribution, expectation and variance of compound random variables
Read: 2.2.1, 2.2.2, 2.2.3, 2.3.1, 2.3.2
• Thursday, 01/30: compound random variable identity, mass function for compound random variables, counting processes, Poisson processes
Read: 2.3.3, 2.3.4, 2.3.5, 3.1.1, 3.1.2, 3.1.3, 3.1.4
• Tuesday, 02/04: Poisson processes, exponential ramdom variables, memeoryless property
Read: 3.1.5, 3.1.6, 3.1.7, 3.1.8, 3.1.9, 3.1.10, 3.1.11, 3.1.12, 3.1.13, 3.2.1, 3.2.2
• Thursday, 02/06: failure/hazard rate function, gamma random variables, law of sum of independent exponential random variables with a common parameter, law of the minimum of independent exponential random variables, probability that minimum of independent exponential random variables is equal to a particular one
• Tuesday, 02/11: inter-arraival time, waiting time, characterization of homogeneous Poisson processes using inter-arraival times, probability that the nth event for a Poisson process N^1 to occur before the m-th event for an independent Poisson propcess N^2
Read: 3.3.1, 3.3.2, 3.3.3, 3.3.5, 3.3.6
• Thursday, 02/13: probability that the nth event for a Poisson process N^1 to occur before the m-th event for an independent Poisson propcess N^2, conditional distribution of arrival times, distribution of inter-arrival times for non-homogeneous poisson processes
• Tuesday, 02/18: Thinning of Poisson processes, sum of independent Poisson processes, compound Poisson processes
Read: 3.4.1, 3.4.2, 3.4.3, 3.4.4, 3.5.1, 3.5.2, 3.5.3, 3.5.4, 3.5.5, 3.5.6, 3.5.7
• Thursday, 02/20:compound Poisson processes, expectation and varaiance of compound Poisson processes, sums of independent compound Poisson processes
• Tuesday, 02/25: Discrete-time Markov chain, Markov property, one-step transition probasbilities, k-step transition probabilities, Chapman-Kolmogorov equation, homogeneous Markov chain, distribution of states, initial distribution
Read: 4.1.1, 4.1.2, 4.1.3, 4.1.4, 4.1.5, 4.1.6, 4.1.7, 4.1.8, 4.1.9, 4.1.10, 4.1.11, 4.1.12, 4.1.13
• Thursday, 02/27: Accessibility of one state from another, communication between states, communication class, ireeducibility, closed subset, absorbing state, period
Read: 4.2.1, 4.2.2, 4.2.3, 4.2.4, 4.2.5, 4.2.6, 4.2.7, 4.2.8, 4.2.9
• Tuesday, 03/03:
• Thursday, 03/05: Review. Test 1 will cover materails from Chapters 2 and 3.
• Tuesday, 03/10: Test 1
Test 1 score distribution for unders : Median: 90, 100: 9,95--99: 6,90--94: 18,85--89: 8,80--84: 4,75--79: 3,70--74: 3, 65--69: 2,60--64: 3,55--59: 1,50--54: 1,45--49: 1,40--44: 1,0--39: 1
Test 1 score distribution for grads : 100: 7,90--94: 2
• Thursday, 03/12: first passge time, first return probability, distribution and mass function of the number of visits to i starting from i, characterization of recurrence and transience using first return probability, characterization of recurrence and transience using k-step transition probabilities, recurrence and transience are class properties, mean time spent in a transient state j starting from a transient state i, first passge probability to a transient state j starting from a transient state i
Read: 4.3.1, 4.3.2, 4.3.3, 4.3.4, 4.3.5, 4.3.6, 4.3.7, 4.3.8,4.3.9, 4.3.10
• Tuesday, 03/24:
• Thursday, 03/26:
• Tuesday, 03/31:
• Thursday, 04/02:
• Tuesday, 04/07:
• Thursday, 04/09: