Stochastic Processes, Markov Chains and Markov Jumps

Name: Stochastic Processes, Markov Chains and Markov Jumps
Rating: 4.0 (234 reviews)

By MJ the Fellow Actuary

Last updated 3/2020

English

What you'll learn

4 sections • 35 lectures • 2h 46m total length

Introduction to Stochastic Processes2:04
Stationary1:56
Increments0:51
Define and explore increments as the change in a stochastic process over time, from single-step to multi-step intervals, and highlight their independence for modeling.
Markov Property2:22
White Noise1:02
Study white noise as a stochastic process where x_t is independently and identically distributed with mean zero. Variance may be nonzero, and the process is stationary with the Markov property.
Random Walk4:33
Explore the random walk defined by x_t = x_{t-1} + e_t, where e_t is white noise, independent increments. It is not stationary; variance grows with time, and drift may occur.
Poisson Distribution3:00
Poisson Process2:50
Compound Poisson Process2:47

Markov Chains1:31
Transition Probabilities3:39
Learn transition probabilities in a Markov chain, denoted p_ij^m(n). Understand transitions between states like healthy, corona, and dead, and crude estimation via N_ij divided by N_i.
Chapman-Kolmogorov Equation1:59
Transition Matrix3:13
Transition Matrix Example with R Code4:48
Explore a transition matrix in a Markov chain, calculating one-, two-, and three-period probabilities of dying from healthy. Implement the calculations in R using a 3x3 matrix and matrix multiplication.
State Modification Trick4:24
Stationary Probability Distributions6:07
Stationary probability distributions describe the long-run distribution of people across states in a Markov chain, using the stationary vector pi and the transition matrix to show stable proportions.
Irreducibility2:41
Periodicity2:01

Installing R and Set up22:14
R basics for Actuaries - Part 114:19
Learn the basics of using R for actuaries, part 1, including installing packages, vectors, sequences, repeats, indexing, for and while loops, if statements, functions, and core statistics.
R basics for Actuaries - Part 213:52
Understanding the Question4:23
Question 1 Solution3:35
Question 2 Solution14:37
Question 3 and 4 Approach2:40
Question 3 Solution6:06
Question 4 Solution7:03
Question 5 Solution1:32
Compare part four to part three to show price frequency lowers taxi frequency, with 17.84% to 12.78% and 5.36 to 4.38 taxis, while cost data govern pods versus taxi choice.

Introduction to Markov Jumps1:37
Transition and Survival Probabilities1:51
Assumptions for Kolmogorov's Forward Differential Equation2:29
Kolmogorov's Forward Differential Equation3:36
Solving Kolmogorov's Forward Differential Equation3:44
Transition Rates and Generator Matrix3:49
Compare Markov chains and Markov jump processes, contrasting discrete-time transition probabilities with continuous-time transition rates, and explain generator matrices, absorbing states, and diagram representations.
Kolmogorov's Backwards Differential Equation7:26

In this course we look at Stochastic Processes, Markov Chains and Markov Jumps

We then work through an impossible exam question that caused the low pass rate in the 2019 sitting.

This question requires you to have R Studio installed on your computer.

Things we cover in this course:

Section 1

Section 2

Section3

Section 4