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Course11110692960 lectures

Probability Theory with Actuarial Applications

Prof. Neelesh S. Upadhye · IIT Madras

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. W1_L1_The Language of Risk Video
  2. W1_L2_The Art of Counting Combinatorics Video
  3. W1_L3_Updating Beliefs Conditional Probability Video
  4. W1_L4_Bayes' Theorem The Update Tool Video
  5. W1_L5_Independence The Free Pass Video

Week 2

  1. W2_L1_From Events to Numbers (Discrete RVs & PMF) Video
  2. W2_L2_The Continuous World (Continuous RVs & PDF) Video
  3. W2_L3_The "Grand Unifier'' (Cumulative Distribution Function) Video
  4. W2_L4_The "Center of Gravity'' (Expected Value) Video
  5. W2_L5_Functions of an RV (The Actuarial Toolkit) Video

Week 3

  1. W3_L1_The "Yes/No'' World (Bernoulli & Binomial) Video
  2. W3_L2_The "Claim Count'' Model (Poisson) Video
  3. W3_L3_The "Waiting Time'' Model (Exponential) Video
  4. W3_L4_The "Flexible'' Model (Gamma) Video
  5. W3_L5_The "Everywhere" Model (Normal Distribution) Video

Week 4

  1. W4_L1_Joint Distributions (Discrete PMF) Video
  2. W4_L2_Joint Distributions (Continuous PDF) Video
  3. W4_L3_Independence & Conditional Distributions Video
  4. W4_L4_Covariance (Measuring Linear Relationship) Video
  5. W4_L5_Correlation & Variance of Sums Video

Week 5

  1. W5_L1_The "1D'' Transformation (The CDF Method) Video
  2. W5_L2_The "1D'' Shortcut (Change of Variable) Video
  3. W5_L3_The "2D'' Transformation (The Jacobian Method) Video
  4. W5_L4_The "Aggregate Loss'' Transformation (Convolution) Video
  5. W5_L5_The "Extreme Loss'' (Order Statistics) Video

Week 6

  1. W6_L1_Conditional Expectation Video
  2. W6_L2_The "Tower Property'' (Law of Total Expectation) Video
  3. W6_L3_The Law of Total Variance (Eve's Law) Video
  4. W6_L4_Conditioning Drills (Mixed Distributions) Video
  5. W6_L5_Review (Compound vs. Mixed Models) Video

Week 7

  1. W7_L1_The "Magic Tool'' (Moment-Generating Function) Video
  2. W7_L2_The MGF "Lookup Table'' Video
  3. W7_L3_The "Payoff'' (MGF of Independent Sums) Video
  4. W7_L4_Advanced Tools (CGFs & Compound Sum MGF) Video
  5. W7_L5_Week 7 Review & Capstone Drill) Video

Week 8

  1. W8_L1_The Problem of "Tails" (Why We Need Bounds) Video
  2. W8_L2_The "Better'' Bound (Chebyshev's Inequality) Video
  3. W8_L3_The Law of Large Numbers (LLN) Video
  4. W8_L4_Other Inequalities (One-Sided Chebyshev & Jensen's) Video
  5. W8_L5_Week 8 Review & Drills Video

Week 9

  1. W9_L1_The Central Limit Theorem (CLT) Video
  2. W9_L2_CLT Drills (Aggregate Loss Problems) Video
  3. W9_L3_The Continuity Correction Video
  4. W9_L4_Capstone Drill (CLT for Aggregate Losses) Video
  5. W9_L5_The Approximation ``Decision Tree'' Video

Week 10

  1. W10_L1_The "Language'' of Insurance Models Video
  2. W10_L2_Policy Feature 1 (Deductibles) Video
  3. W10_L3_Policy Feature 2 (Policy Limits) Video
  4. W10_L4_Capstone (Pricing a ``Policy Layer'') Video
  5. W10_L5_Review & Introduction to Stop-Loss Video

Week 11

  1. W11_L1_The "Master Formula" for Expected Aggregate Loss Video
  2. W11_L2_The "Master Algorithm" for Var(S) Video
  3. W11_L3_Finding Severity Moments E[Y^2] and Var(Y) Video
  4. W11_L4_The "Master Algorithm'' Drill Video
  5. W11_L5_Week 11 Review & Capstone Drills Video

Week 12

  1. W12_L1_''The Big Picture'' Review (Part 1: The Toolkit) Video
  2. W12_L2_''The Big Picture'' Review (Part 2: The Models) Video
  3. W12_L3_Mock Exam Review (Part 1: Q1--10) Video
  4. W12_L4_Mock Exam Review (Part 2: Q11--20) Video
  5. W12_L5_Mock Exam Review (Part 3: Q21--30) Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Mathematics
Teacher
Prof. Neelesh S. Upadhye
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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