Module 16:
Inequalities, convexity and tail bounds

Module 16

What this module is for

Both for basic bounds and Jensen; advanced concentration mainly for QR. Teach what can be established without knowing the full distribution.

Lesson 16.1 · Core

Markov, Chebyshev and one-sided bounds

Depth: Working proficiency

QT/QR relevance: Both; controlling uncertainty with limited information

Lesson 16.2 · Core

Jensen’s inequality and nonlinear expectations

Depth: Interview mastery

QT/QR relevance: Both; nonlinear payoffs and decision criteria

Lesson 16.3 · Core · QR Extension

Cauchy–Schwarz and covariance constraints

Depth: Working proficiency; proof-based variants at researcher depth

QT/QR relevance: Both, especially QR; valid risk relationships

Lesson 16.4 · Research Depth

Chernoff and Hoeffding bounds

Depth: Advanced / quant researcher depth — Extension

QT/QR relevance: QR; finite-sample probability guarantees

Assessment

Module 16 assessment

Open assessment · No submitted assessment yet