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Knowledge is the only good; ignorance the only evil. Socrates

I can only understand things after I’ve thought about them for ages and made them very, very simple. John Conway

Featured Posts

About | –> Reading since 1990 | PMIR | Conditional Probability | PIR Errata

2025-26 Posts by Date

DRAFT Gold, Liquid, and Soft: Relativistic Chemistry, Band Structure, and Conduction

Why is gold gold, mercury liquid and lead soft?

Aug 18, 2025

Memorizing the Periodic Table

Memorizing the periodic table up to Lawrencium: blending rote memorization and figuring things out.

Aug 18, 2025

Intraterrestrials

The hunt for life beneath earth’s surface—and how new discoveries are challenging our most basic…

Aug 16, 2025

ATP — Life’s Universal Energy Currency

ATP powers life’s work. It is the primary chemical form of usable energy in all known organisms;…

Aug 12, 2025

Elements

Properties of the elements in charts and tables.

Aug 10, 2025

Sapiens

Notes on Harari’s book, Sapiens.

Aug 7, 2025

Electrons and Spherical Harmonics

Chatters and I have been learning about electrons and elements.

Aug 3, 2025

Python Logging

7 min

programming

As you may know, I’m a huge fan of Python. I’ve been programming in it for over 10 years, and I…

Jul 30, 2025

Cats and Dogs

6 min

notes

llm

Clades for cats and dogs.

Apr 8, 2025

Prehistory

Human history before the written record including timelines and clades of human evolution.

Apr 8, 2025

Declination, obliquity, and all that

12 min

notes

astronomy

Definitions, etymology and values of parameters and terminology related to orbits.

Apr 7, 2025

Fairness in Insurance Pricing

7 min

notes

Fair insurance pricing should be ensured by disclosure not rate regulation.

Apr 7, 2025

Not like us

6 min

notes

llm

Gen AI and LLM’s are amazing, but occasionally offer a glimpse into how their intelligence differs…

Apr 7, 2025

Earth’s and Moon’s Orbits

8 min

notes

astronomy

Finding the Moon and understanding its cycles.

Apr 4, 2025

Beers

6 min

notes

Beer, ale, larger, stout: what’s the difference?

Apr 2, 2025

Orbits and Kepler’s Third Law

An overview Kepler’s third law of planetary motion.

Mar 28, 2025

Rocks

The whole world is literally built on rocks.

Mar 28, 2025

1 meter is the median size in the Universe

9 min

notes

Human scale is about the middle of the range of logarithmic sizes.

Mar 12, 2025

Going Spectral

Going Spectral: Why and how to implement spectral pricing challenges the constant cost of capital…

Feb 23, 2025

The Class of Bar-Lev–Enis–Tweedie Distributions

The class of power-variance family distributions jointly discovered by Bar-Lev and Enis, and…

Feb 6, 2025

Inverting Characteristic Functions Using FFTs

45 min

notes

How to use FFTs to invert the characteristic function of a probability distribution.

Jan 23, 2025

PIR Book Examples in Aggregate

2 min

programming

pir

Python code to recreate exhibits from Pricing Insurance Risk book.

Jan 15, 2025

Better Markdown Snippets

1 min

meta

blog

Pithier markdown tips—just the things I forget…

Jan 13, 2025

Drawing with MidJourney

1 min

meta

Learning to use MidJoureny effectively.

Jan 13, 2025

Stable Distributions

4 min

notes

Tail and body behavior of stable distributions.

Jan 13, 2025

Fibonacci Chest—woodwork project No. 3

1 min

about

woodwork

An open frame chest with an oak frame, top, drawer runners and pulls, built in 2004. Hard maple…

Jan 1, 2025

Bowl Database

2 min

about

woodwork

This page is searchable database of the 149 bowls I turned between 2010 and 2017. The bowls are…

Dec 31, 2024

Reading in 2024

2024: the year of the Very Short Introduction!

Dec 31, 2024

Why I like Python

3 min

Python

programming

I ~~like~~ love Python the language. The libraries are a bonus and the reason I use Python. Here are a…

Nov 27, 2024

Classifying and Identifying Trees

4 min

notes

trees

Introduction to multipart-post on tree classification and Introduction.

Oct 19, 2024

Extreme Tails of the Normal Distribution

5 min

notes

probability

Estimating extreme quantiles of the normal distribution.

Jun 22, 2024

What I Ask GPT

26 min

notes

llm

How GPT helped me cluster the questions I’ve asked it over the last year.

Jun 2, 2024

Potted Measure Theory

A quick summary of measure theory on the real line.

May 22, 2024

Energy Intensity of Internet Traffic

8 min

notes

llm

How much energy is required to transfer 1GB of data over the internet from London to Paris?

May 21, 2024

Science and Pseudo-science

13 min

notes

llm

This post is another comparison of LLMs. I asked for a summary of Popper’s philosophy…

May 19, 2024

The Forgetting Curve

3 min

notes

llm

The forgetting curve is a concept that describes how the ability to recall information decreases…

May 19, 2024

Trees

16 min

notes

llm

LLM guided tree classification.

May 19, 2024

Defining Bullshit

3 min

notes

llm

LLM definitions of Bullshit.

May 9, 2024

Joplin-Evernote Migration Policy

7 min

about

llm

LLM’s offer advice on maintaining historical notes.

May 8, 2024

Non-Measurable Sets

Detailed construction of a non-Lebesgue measurable set, per Halmos.

May 3, 2024

Doob’s Upcrossing Lemma

Doob’s optional stopping theorem is a fundamental result in probability theory, particularly in…

May 2, 2024

Geometric Brownian Motion, Yet Again!

2 min

notes

probability

A heuristic explanation of geometric Brownian motion

May 2, 2024

Waiting Time for a Random Walk to Hit One

1 min

notes

Let \(X_n\) be a symmetric random walk moving up or down by one at each step with equal…

May 2, 2024

The Incurred Loss Process

Towards a theory of incurred loss processes, starting with a review of stochastic processes.

Apr 27, 2024

Reinsurance Decision Making

What’s wrong the the constant cost of capital assumption

Apr 23, 2024

Why Go Spectral?

Why and how to use insurance spectral pricing methods.

Apr 16, 2024

Compensators

Given an exponential random variable \(T\) with the hazard function \(\alpha(t) = t\), the…

Apr 12, 2024

Conditional Expectations Given The Sum of Independent Random Variables with Regularly Varying Densities

7 min

notes

Summary of results and examples from a recent paper of Denuit et al.

Apr 4, 2024

Hosting Documentation on GitHub Pages

8 min

meta

llm

Another comparison of LLMs.

Mar 24, 2024

File Consolidator

1 min

meta

Rationalizing years of file archives

Mar 20, 2024

LLM Comparison: Managing Sublime Text Projects

6 min

notes

llm

Gemini, GPT, and Claude answer questions about Sublime Text

Mar 20, 2024

LLM Comparison: Why Buy Insurance?

Editing and tidying up transcribed text using LLMs.

Mar 20, 2024

Large Cardinals and Set Theory

What can “large cardinals” have to do with Lebesgue measurable sets? I asked Chat GPT to find out…

Mar 20, 2024

MJ Images

1 min

meta

Retrieving and processing Midjourney images.

Mar 20, 2024

Markdown snippets

Handy Quarto markdown tips and techniques that are easy to forget (=I forget them).

Mar 20, 2024

Using TikZ in a blog page

1 min

meta

blog

Using great2 to process tikz into svg files for blog posts.

Mar 20, 2024

Conditional Probability

\[ \def\E{\mathsf E} \def\A{\mathscr A} \def\B{\mathscr B} % for general sigma…

Mar 19, 2024

Gas

21 min

notes

llm

The ideal gas model and when it fails.

Mar 19, 2024

How a Pneumatic Tire Works

33 min

about

llm

A car tire supports the weight of the car by the difference in tension in the top and bottom tire…

Mar 18, 2024

Ice

11 min

about

llm

Table showing different types of ice.

Mar 12, 2024

Insurance in the Arts

3 min

about

llm

Cases where insurance could change the plot in famous literature.

Mar 12, 2024

Midjourney Prompts

3 min

about

llm

Mention specific art styles, techniques, artists, or art movements.

Mar 12, 2024

Evensong Order of Service

4 min

about

Church of England Evensong Order of Service

Mar 6, 2024

Hyphens

2 min

about

llm

Chat GPT’s instructions on the use of hyphens.

Mar 2, 2024

Words

Technical words from VSIs

Feb 28, 2024

Knowledge in Diagrams

2 min

about

A collection of explanatory diagrams

Feb 27, 2024

Ages of the Earth

Earth and human timelines.

Feb 26, 2024

VSI Series

List of Very Short Introduction Books.

Feb 24, 2024

Numpy meshgrid

2 min

Python

programming

This always confuses me. Here’s the help on meshgrid:

Feb 23, 2024

Matplotlib: tips and tricks

Here are several things I always forget when using matplotlib. This post written with help from…

Feb 21, 2024

Podcast and Video Appearances

1 min

about

presentations

I have appeared as a guest on several podcasts and videos. See also my YouTube videos.

Feb 18, 2024

Reading Since 1990

1 min

about

reading

A searchable table of all the books I have read since 1990.

Feb 18, 2024

Quarto YAML and Markdown: tips and tricks

What I learned today by RTFD.

Feb 14, 2024

Chat GPT and Google Gemini Answer Programming Questions

I believe that large language models (LLMs) are the most amazing thing that has happened in my…

Feb 13, 2024

Effective Python: Classes

Object oriented programming in Python

Feb 13, 2024

My Shelf of Favorite Books

5 min

about

Contents and history of my shelf of favorite books since 2003.

Feb 13, 2024

Catastrophes Ranked by Energy

Code Snippets

3 min

programming

Python

int('000000007fff4070', base=16)

Feb 7, 2024

Effective Python: R Style Regression

I use R, but I love Python. However, let’s face it, basic linear regression in R is very…

Feb 7, 2024

The Cost of Goods Sold

John Major and Stephen Mildenhall, CARe Meeting, June 9, 2021

Feb 7, 2024

Presentations Since 1996

12 min

about

presentations

Conference, meeting, and online talks and presentation since 1997.

Jan 1, 2024

Publications

1 min

about

publications

Journal articles, books, popular press, and working papers.

Jan 1, 2024

Resume

3 min

about

Professional and academic experience.

Jan 1, 2024

Abstracts from Mario Ghossoub’s Papers on Risk

Effective Python: Floats

I studied math(s) for 9 years as a undergraduate and graduate student. I never came across a…

Oct 6, 2022

Effective Python: Building a Test DataFrame

It is often helpful to have a test dataframe. This function makes one with several optional…

Jul 5, 2022

Effective Python: Introspection

Get the arguments of a function. Used in aggregate.distr.Aggregate.

Jul 5, 2022

Effective Python: Munging Fitbit Data with Pandas

Pain lies at the intersection of the computer and the real-world. Real-world data is messy…

Jun 28, 2022

Reinsurance Optimization Literature Review

Catastrophe reinsurance provides insurance companies protection against excessive losses caused by…

May 11, 2022

Effective Python: Projects

The best way to learn Python is to use it to solve a real-life problem you face. I’m often asked…

Apr 5, 2022

Bon Pint

2 min

actuarial review

The nerdier regulars at the Bon Pint pub enjoy a peculiar number game. They start with an integer \…

Mar 30, 2022

Academic Descriptions of Risk

3 min

notes

risk

Equal probability lotteries \([a, b]\) describe outcomes \(a\) and \(b\), which can be fixed or…

Mar 15, 2022

Reinsurance Capital or Credential

Reinsurance: Capital or Credential?

Mar 15, 2022

Effective Python: Importing Data into Pandas

Problems arise when computers interact with the real world. You step out of a controlled…

Mar 11, 2022

ZFC Axioms

2 min

notes

The Zermelo-Frankel axioms of set theory: extension, foundation, pairing, union, power, infinity…

Mar 11, 2022

Non Bayesian Risk

Distortion risk measures

Mar 7, 2022

David Wright Notes

18 min

notes

What is the insurance business? What do you manufacture? I asked that question to a lot of people…

Mar 2, 2022

When is Premium Riskier Than Loss Slides

PIRC presentation comparing volatility from premium and loss uncertainty.

Mar 2, 2022

CEOs Talk About Risk

In my judgment, the calendar year or published combined ratio is the primary measure of…

Mar 1, 2022

Effective Python: Converting Datatypes in Pandas

Series method astype it is already a number and you want to change the type. Will not coerce.

Mar 1, 2022

Towards the Quantitative Analysis of Quantitative Factors

process risk; param risk; winner’s curse; PAT; ambiguity; morale hazard; info asymmetry

Feb 28, 2022

Effective Python: Dates

Problems arise when computers interact with the real world. You step out of a controlled…

Feb 20, 2022

Effective Python: `requests`, `BeautifulSoup`, and web scraping

The requests library does for web interaction what pathlib.Path path does for files.

Feb 20, 2022

Risk and Return

There are no universally true statements about risk.

Feb 20, 2022

Effective Python: Introspection with Pandas

This code defines a function that extracts all an objects properties into a pandas dataframe. It…

Feb 15, 2022

Effective Python: Strings and Unicode

Ever cut and paste text between applications and get unexpected results? Particularly when the…

Feb 15, 2022

Effective Python: `zip`, `enumerate`, and `iter`

This short post looks at three built-in Python functions: zip, enumerate, and iter.

Feb 15, 2022

Effective Python: Files

If you write a program of any length, you will likely have to manipulate files and filenames.…

Feb 10, 2022

Hash Magic Encryption and Digital Signatures

9 min

notes

Hash functions are miraculous, helpful tools we have no right to expect to exist. They seem far…

Feb 8, 2022

Creating TeX Format Files

3 min

meta

blog

Creating a TeX format file for faster processing.

Feb 4, 2022

Cartograms

Wordle the Best Start

ConvexConsiderations Quarto Blog Setup

Defines containing folder

Jan 31, 2022

Active and Inactive Research

Effective Python Outline

A series of posts about effective Python programming for the intermediate user.

Jan 20, 2022

Effective Python: Regular Expressions

Regular expressions are a wonderful shorthand way to select and manipulate strings.

Jan 20, 2022

Effective Python: Setting up Python Environments

1 min

programming

Python

Notes I found helpful setting up my Python environments.

Jan 20, 2022

Markdown

1 min

meta

The text in this box becomes the description for the page.

Jan 20, 2022

Modes of Convergence

6 min

notes

probability

Random variables can converge in several different ways. Here is a brief introduction…

Jan 20, 2022

Pricing Insurance Risk Book

Contents, errata, and other information about Pricing Insurance Risk, my book written with John…

Jan 20, 2022

Pricing Seasonal Peril Catastrophe Bonds: A Simplified Approach

We show a catastrophe bond’s economically meaningful cash flows are the same as a fully continuous…

Jan 20, 2022

Similar risks have similar prices: A useful and exact quantification

This paper introduces an straightforward algorithm to determine a range of prices consistent with…

Jan 20, 2022

About

3 min

about

About me and the blog

Jan 1, 2022

Pricing Insurance Risk Course (PIRC)

This course explains modern approaches to pricing insurance risk, the process of setting a…

Dec 31, 2021

The Aggregate Package

The aggregate Python package makes working with aggregate loss distributions easy.

Dec 31, 2021

When is Premium Riskier Than Loss

1 min

An analysis of US statutory insurance data since 1992 shows that premium is more uncertain and…

Nov 30, 2021

A Modern Approach to Pricing for Risk

1 min

presentations

Liberty Mutual, November 2021

Nov 15, 2021

Bodoff’s Percentile Layer of Capital-Method

22 min

research

pricing

Bodoff’s paper¹ describes a new approach to capital allocation; the catalyst for this new approach…

Jan 31, 2021

Equilibrium Risk Pools

This research investigates equilibrium risk pools in a market with risk-based solvency regulation…

Oct 21, 2020

Minimum Bias and Exponential Family Distributions

This post introduces four short expository notes describing exponential family distributions that…

Oct 21, 2020

Bailey Simon Minimum Bias Reexamined

Part I of a four part series “Minimum Bias and Exponential Family Distributions”.

Oct 20, 2020

Exponential Family Distributions

Part II of a four part series “Minimum Bias and Exponential Family Distributions”.

Oct 20, 2020

Probability Models for Insurance Losses

Part III of a four part series “Minimum Bias and Exponential Family Distributions”.

Oct 20, 2020

The Tweedie Power Variance Function Family

Part IV of a four part series “Minimum Bias and Exponential Family Distributions”.

Oct 20, 2020

Charging for Diversifiable Risk and Proud to Do It

1 min

presentations

John Major and Stephen Mildenhall, CAS Webinar, September 24, 2020.

Sep 24, 2020

Teaching

2 min

notes

teaching

From 2016-2020 I was Assistant Professor in the School of Risk Management, Insurance, and…

Aug 31, 2020

How to Allocate Capital if You Really Must

1 min

presentations

John Major and Stephen Mildenhall, CAS Spring Meeting, May 13, 2020

May 13, 2020

Spectral Risk Measures and Applications in Insurance ERM

1 min

presentations

John Major and Stephen Mildenhall, ASTIN Special Interest Webinar, March 25, 2020

Mar 25, 2020

ERM Saves the Day for the CEA

72 min

research

pricing

Abstract. Since its emergence in the 1990s enterprise risk management (ERM) has struggled to…

Oct 28, 2019

ERM Saves the Day for the CEA v2

72 min

research

pricing

Abstract. The California Earthquake Authority (CEA) became operational December 1, 1996. It was…

Aug 7, 2019

AI and Insurance

1 min

presentations

New AI techniques help computers solve problems that people find easy but that computers have…

May 20, 2019

Life Insurance Backdating

16 min

research

Assuming continuous rating the insured is always worse off with backdating on a net basis. A net…

Apr 15, 2019

Programming Your Career

I love to program, and I am convinced programming has been beneficial to my career. Other…

Jan 7, 2019

Blockchain and Insurance

1 min

presentations

Blockchain solves trust problems. If you trust your counter-parties, or operate in a country with…

Nov 13, 2018

Business Risk and Analytics

33 min

notes

risk

There is a synergistic relationship between business, analytics, and technology (the BAT triangle)…

Sep 15, 2018

Frequency Distributions

3 min

notes

probability

A random variable \(N\) is \(G\)-mixed Poisson if \(N\mid G\) has a Poisson \(nG\) distribution…

Sep 15, 2018

Summary of Insurance Priority Laws and Statutes

101 min

notes

insurance

Upon the issuance of a proper court order placing a domestic insurer in receivership or placing a…

Jul 19, 2018

In Praise of VaR Part II

“Can he have everything louder than everything else?” Ian Gillan, Deep Purple, Made In Japan

Jan 16, 2018

The Insurance Stack in a Disrupted World

DRAFT / work in progress!

Nov 15, 2017

In Praise of VaR Part I

VaR can misbehave,
Hiding dragons in the tail.
Many views reveal.

Nov 13, 2017

FinTech and InsurTech

1 min

presentations

Billions of dollars are flowing into new FinTech and InsurTech start-ups. How do these companies…

Nov 10, 2017

Bowls

1 min

about

woodwork

I have turned 149 bowls from a variety of North American woods.

Sep 1, 2017

Woodworking

1 min

about

woodwork

Between 2004 and 2013, I was a sporadically active woodworker with a basement shop.

Aug 31, 2017

Learning Objectives

64 min

notes

teaching

Learning objectives have three components:

May 17, 2017

Election Day Lessons for the Data Scientist

Kim Hypothetical, FCAS, is a pricing actuary in the Large Accounts department at Hypothetical…

Jan 22, 2017

The Black-Scholes Option Pricing Formula

I had been fascinated by Black-Scholes since a fellow student at the University of Chicago math…

Sep 24, 1997

Wang’s Proportional Hazard Transform

Early description and exploration of the exciting (then) new Wang transform to my colleagues at…

Aug 27, 1997

Modeling Loss Ratios for Aggregate Features

Very early work on aggregate loss distributions! From the introduction:

May 22, 1997

Premium Margins and Managing the Catastrophe Risk

I applied the method to different lines of business, based on A.M. Bests’ aggregates and averages…

Aug 22, 1995

A Note on Elkies’ Proof

1 min

notes

research

This is a short three-page note on Elkies’ proof that an elliptic curve has infinitely many…

Mar 1, 1992

Categories

Featured Posts

2025-26 Posts by Date

Reading in 2026

Pricing Multi-Period Insurance Risk

Comonotonicity and Pareto Optimality

Factoring Integers After The Dark Ages

Mutual and Reciprocal Insurers

Brownian and Poisson Filtrations

Borel, Wiener, Poisson, Kuratowski, etc.

Convergence and Counter-Examples for Risk Measures

Spectral Risk Measures are not Weak Acceptance Time Consistent

Top Five Insurer Market Cap vs. S&P 500

Permutations and the 100 Prisoner Problem

On Submultiplicative Distortions

7 Powers

Contracts with Contingent Cash Flows

Representing Distortions: A Circle of Equivalences

Reading in 2025

Bernoulli and Uniform Random Variables

What is Information?

What is a Country?

The Periodic Table Again

Atomic Weights

aligned or align?

Inequality: Causes, Consequences, and Perspectives

Cats’ View of Humans

Dogs’ View of Humans

Oxygen Producers

The Mind Between

Reciting the Elements

JavaScript for Recitation Testers

Minerals

Acids and Bases

An Earth of Bacteria

File Database Part I - Python Speedup

File Database Part II - Rust and Low Level OS Calls

DNS Records

Rehosting my websites

Setting up a VPS

Elements II

Geography, Institutions, and Culture

Living Well

Oxidation and Redox

Powerful Words: The ZF Axioms

The Agrarian Revolution and Roots of Inequality

Cacti

DRAFT Gold, Liquid, and Soft: Relativistic Chemistry, Band Structure, and Conduction

Memorizing the Periodic Table

Intraterrestrials

ATP — Life’s Universal Energy Currency

Elements

Sapiens

Electrons and Spherical Harmonics

Python Logging

Cats and Dogs

Prehistory

Declination, obliquity, and all that

Fairness in Insurance Pricing

Not like us

Earth’s and Moon’s Orbits

Beers

Orbits and Kepler’s Third Law

Rocks

1 meter is the median size in the Universe

Going Spectral

The Class of Bar-Lev–Enis–Tweedie Distributions

Inverting Characteristic Functions Using FFTs

PIR Book Examples in Aggregate

Better Markdown Snippets

Drawing with MidJourney

Stable Distributions

Fibonacci Chest—woodwork project No. 3

Bowl Database

Reading in 2024

Why I like Python

Classifying and Identifying Trees

Extreme Tails of the Normal Distribution

What I Ask GPT

Potted Measure Theory