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Home

Convex Considerations blogs anything I find interesting or want to remember.

Featured Posts

Reading since 1990 | Markdown snippets | Conditional probability | Trees

All Posts by Date

About

About me and the ConvexConsiderations blog

Reading in 2024

2024: the year of the Very Short Introduction!

Phylogenetic Tree for Common Species

Phylogenetic tree for tree species common in the UK.

Common Names

Database of mapping between Latin name and common name.

Tree Seeds

Tree seeds collected around London.

Phylogenetic Trees for All Tree Species

Phylogenetic tree diagrams for most orders containing trees.

Phylogenetic Trees for Common Tree Species

Phylogenetic tree diagrams for orders containing more common tree species.

Common Trees

Table of characteristics of tree species common in the UK and US.

Common Trees Pivot Table

Pivot table of characteristics of tree species common in the UK and US.

Classifying and Identifying Trees

How to classify and identify trees.

General Classification

General background on plant classification.

Tree Classification

Basics tree classification including lists of common orders, families, genera, and species with…

Tree Identification

Basics techniques to identify trees.

Tree Identification: Pictures

Pictures and schematics to help identifying trees.

General Botany

General botany background for tree identification, including parts of a flower, plant sex, and…

Lexicon

Lexicon of Latin and other common technical terms used to describe trees.

Galaxies VSI

The age of the Universe is determined by studying the largest things using general relativity. The…

Tame Case Study PIR Exhibits

Tame Scenario PIR Case Study Exhibits

Case Studies from Pricing Insurance Risk

An introduction to the four case studies from PIR.

Creating a Custom Case Study

How to customize the PIR case study exhibits for your own scenario using aggregate.

Pricing Insurance Risk Book Errata

Errata list of PIR. Report issues to mynl@me.com.

Extreme Tails of the Normal Distribution

Estimating extreme quantiles of the normal distribution.

Chemistry VSI

Bonds: ionic, covalent, metallic; reactions: proton transfer, electron transfer, radical, Lewis…

Particle Physics VSI

There are seventeen fundamental particles: six quarks, six leptons, and five bosons.

Plate Tectonics VSI

Lithosphere takes tens of millions of years to warm up when subducted into the asthenosphere.

What I Ask GPT

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

Potted Measure Theory

A quick summary of measure theory on the real line.

Energy Intensity of Internet Traffic

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

Geography VSI

Space, place, and environment.

Science and Pseudo-science

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

The Forgetting Curve

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

Trees

LLM guided tree classification.

Defining Bullshit

LLM definitions of Bullshit.

Joplin-Evernote Migration Policy

LLM’s offer advice on maintaining historical notes.

Conditional Probability: Background Material

Probability background material with LLM assistance.

Conditional Probability: Other Stuff

More notes on conditional probability.

Non-Measurable Sets

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

Doob’s Upcrossing Lemma

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

Geometric Brownian Motion, Yet Again!

A heuristic explanation of geometric Brownian motion

Waiting Time for a Random Walk to Hit One

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

A. Probability Background

Probability background for ILPs

B. Stochastic Processes

Definitions and properties of stochastic processes

C. General Examples

Archetypal examples of stochastic processes

D. ILP Examples

Finally, we reach the subject under discussion!

The Incurred Loss Process

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

Reinsurance Decision Making

What’s wrong the the constant cost of capital assumption

Why Go Spectral?

Why and how to use insurance spectral pricing methods.

Compensators

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

Human Evolution VSI

Out of Africa or multiregional?

Keynes VSI

Economists should strive to be as useful as dentists.

Stars and The Sun VSIs

We are all made of atoms created in stars!

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

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

The First World War VSI

“At the end of 1917 the prospects for the Allies still looked grim.”

Climate and Climate Change VSIs

“IPCC 2021 states that the evidence for climate change is unequivocal, and there is a very high…

Hosting Documentation on GitHub Pages

Another comparison of LLMs.

File Consolidator

Rationalizing years of file archives

LLM Comparison: Managing Sublime Text Projects

Gemini, GPT, and Claude answer questions about Sublime Text

LLM Comparison: Why Buy Insurance?

Editing and tidying up transcribed text using LLMs.

Large Cardinals and Set Theory

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

MJ Images

Retrieving and processing Midjourney images.

Markdown snippets

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

Using TikZ in a blog page

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

Conditional Probability

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

Gas

The ideal gas model and when it fails.

Weather VSI

Different types of cloud.

How a Pneumatic Tire Works

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

Isotopes VSI

Same on the outside but different on the inside; detect one atom in \(10^{-15}\); cosmogenic creation

Accounting VSI

The earliest human written records are all accounts; expenses use assets so are entered on the…

Earth System Science VSI

The Earth has experienced huge changes over very long time frames but feedback induced stability…

Geophysics VSI

Global Catastrophes VSI

Meteorites will kill us…or maybe a volcano or our own stupidity. Landslides could flood the US…

Ice

Table showing different types of ice.

Insurance in the Arts

Cases where insurance could change the plot in famous literature.

Magna Carta VSI

Charters were common; John was a really bad king; original MC included enforcement by 25 barons.

Midjourney Prompts

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

Newton VSI

Newton: scientist, alchemist, anti-Trinitarian, MP, Master of the Mint.

Planets VSI

The asteroid Apophis will have a close encounter with the Earth miss on 2029-04-13, which is a…

Risk VSI

Normative - descriptive - prescriptive: What should we do? What do we do? How can we improve?

Statistics VSI

The technology of extracting meaning from data and of handling uncertainty. Mechanistic vs…

The Earth VSI

The Earth was very different a long time ago; microbes under the seafloor; paleomagnetism and…

The Ice Age VSI

Ice bergs or ice sheets debate; seabed and ice cores; Milankovitch’s three cycles; global impact…

The Laws of Thermodynamics VSI

Temperature: most probable distribution over available states; conservation of energy; entropy…

The Period Table VSI

Potassium-Argon reversal. Where should hydrogen appear? Why the actinides and lanthanides appear…

Tides VSI

Almost everything you know about tides is irrelevant to how they actually work! It’s all about…

Evensong Order of Service

Church of England Evensong Order of Service

Hyphens

Chat GPT’s instructions on the use of hyphens.

Words

Technical words from VSIs

Knowledge in Diagrams

A collection of explanatory diagrams

Ages of the Earth

Earth and human timelines.

VSI Series

List of Very Short Introduction Books.

Numpy meshgrid

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

Matplotlib: tips and tricks

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

Podcast and Video Appearances

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

Reading Since 1990

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

Quarto YAML and Markdown: tips and tricks

What I learned today by RTFD.

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…

Effective Python: Classes

effective python

Object oriented programming in Python

My Shelf of Favorite Books

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

Catastrophes Ranked by Energy

Add summary here…

Code Snippets

int('000000007fff4070', base=16)

Effective Python: R Style Regression

effective python

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

The Cost of Goods Sold

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

Cat/Non-Cat Case Study PIR Exhibits

Cat/Non-Cat Scenario PIR Case Study Exhibits

Discrete Case Study PIR Exhibits

Discrete scenario PIR Case Study exhibits

Discrete Case Study PIR Exhibits

Discrete scenario PIR Case Study exhibits

HU/Severe Convective Storm Aggregate Case Study PIR Exhibits

HU/Severe Convective Storm with aggregate reinsurance scenario PIR Case Study exhibits

Presentations Since 1996

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

Publications

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

Resume

Professional and academic experience.

Abstracts from Mario Ghossoub’s Papers on Risk

Ghossoub’s Website

Effective Python: Floats

effective python

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

Effective Python: Building a Test DataFrame

effective python

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

Effective Python: Introspection

effective python

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

Effective Python: Munging Fitbit Data with Pandas

effective python

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

Reinsurance Optimization Literature Review

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

Effective Python: Projects

effective python

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

Bon Pint

actuarial review

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

Academic Descriptions of Risk

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

Reinsurance Capital or Credential

Reinsurance: Capital or Credential?

Effective Python: Importing Data into Pandas

effective python

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

ZFC Axioms

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

Non Bayesian Risk

Distortion risk measures

David Wright Notes

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

When is Premium Riskier Than Loss Slides

PIRC presentation comparing volatility from premium and loss uncertainty.

CEOs Talk About Risk

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

Effective Python: Converting Datatypes in Pandas

effective python

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

Towards the Quantitative Analysis of Quantitative Factors

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

Effective Python: Dates

effective python

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

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

effective python

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

Risk and Return

There are no universally true statements about risk.

Effective Python: Introspection with Pandas

effective python

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

Effective Python: Strings and Unicode

effective python

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

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

effective python

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

Effective Python: Files

effective python

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

Hash Magic Encryption and Digital Signatures

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

Creating TeX Format Files

Creating a TeX format file for faster processing.

Cartograms

Wordle the Best Start

Wordle is a popular word game. You have six chances to guess a five-letter word. For each guess…

ConvexConsiderations Quarto Blog Setup

Defines containing folder

Active and Inactive Research

Back Cover of Pricing Insurance Risk

Back cover “blurb” from PIR.

Effective Python Outline

effective python

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

Effective Python: Regular Expressions

regular expressions

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

Effective Python: Setting up Python Environments

Notes I found helpful setting up my Python environments.

Markdown

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

Modes of Convergence

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

Pricing Insurance Risk Book

Pricing Insurance Risk (PIR), written with John Major, describes the last mile of underwriting.…

Pricing Insurance Risk Presentations and Videos

Presentations and videos related to PIR.

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…

Similar risks have similar prices: A useful and exact quantification

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

Pricing Insurance Risk Course (PIRC)

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

The Aggregate Package

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

When is Premium Riskier Than Loss

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

A Modern Approach to Pricing for Risk

Liberty Mutual, November 2021

Bodoff’s Percentile Layer of Capital-Method

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

Equilibrium Risk Pools

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

Minimum Bias and Exponential Family Distributions

exponential family

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

Bailey Simon Minimum Bias Reexamined

actuarial review

exponential family

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

Exponential Family Distributions

exponential family

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

Probability Models for Insurance Losses

exponential family

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

The Tweedie Power Variance Function Family

exponential family

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

Charging for Diversifiable Risk and Proud to Do It

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

Teaching

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

How to Allocate Capital if You Really Must

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

Spectral Risk Measures and Applications in Insurance ERM

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

ERM Saves the Day for the CEA

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

ERM Saves the Day for the CEA v2

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

AI and Insurance

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

Life Insurance Backdating

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

Programming Your Career

actuarial review

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

Blockchain and Insurance

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

Business Risk and Analytics

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

Frequency Distributions

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

Summary of Insurance Priority Laws and Statutes

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

In Praise of VaR Part II

actuarial review

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

The Insurance Stack in a Disrupted World

DRAFT / work in progress!

In Praise of VaR Part I

actuarial review

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

FinTech and InsurTech

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

Bowls

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

Woodworking

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

Learning Objectives

Learning objectives have three components:

Election Day Lessons for the Data Scientist

actuarial review

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

The Black-Scholes Option Pricing Formula

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

Wang’s Proportional Hazard Transform

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

Modeling Loss Ratios for Aggregate Features

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

Premium Margins and Managing the Catastrophe Risk

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

A Note on Elkies’ Proof

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

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Stephen J. Mildenhall. License: CC BY-SA 2.0.

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