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Featured

Overview of Ledger's Modeling

Blurry Images and Hierarchical Models

We share a series of blurry images and ask you, the reader, to make some predictions about those pictures. We then use this series of examples to illustrate the power and value of hierarchical modeling.
#featured #level-beginner #philosophy
Overview of Ledger's Modeling

Ledger's Modeling Philosophy

Ledger Investing does not use actuarial science to price risk. We explain why we don't, and provide an intuitive justification of our alternate method through an analogy to a fund of funds.
#level-beginner #philosophy
Casualty Insurance Industry Overview

Line of Business Development Patterns

When an insurance company issues a policy, the company knows the amount of premium it will receive, but it may not know for many years exactly how much it will cost to settle all of the claims associated with that policy. The study of patterns of claims emergence and loss payments is called loss development. We illustrate a few of the key characteristics of loss development and how it varies by statutory line of business and by company. Finally, we look at the relationship between the length of time it take for losses to develop and the degree of uncertainty surrounding the ultimate value of those losses.
#industry-analysis #level-beginner #featured
Casualty Insurance Industry Overview

Line of Business Loss Ratio Behavior

The core measure of an insurance company's performance is its loss ratio. We describe what loss ratios are, and how they tend to behave. We explore how loss ratios vary by line of business, and what types of variation in behavior are typical. Finally, we explore the root causes behind why different lines of business have different loss ratio behavioral characteristics.
#industry-analysis #level-intermediate #featured

Industry Analysis

Casualty Insurance Industry Overview

Casualty Insurance Lines of Business

Property & casualty insurance includes a wide number of distinct insurance products with widely varying characteristics. We describe what, fundamentally, property & casualty insurance covers. Property & casualty insurance products are grouped into lines of business for statutory reporting purposes. We describe what these lines of business are and why they are difficult to pin down precisely.
#level-beginner #industry-analysis
Casualty Insurance Industry Overview

Property & Casualty Insurance Companies

We look at basic features of insurance companies by exploring statutory filings data. We see how many property & casualty insurance companies there are, and how insurance groups are formed of clusters of insurance companies. We also look at the size distribution of insurance companies, and discuss reinsurance strategies of different insurance companies.
#level-beginner #industry-analysis
Casualty Insurance Industry Overview

Line of Business Volume and Diversification

The US property & casualty industry is subdivided into 22 separate lines of business in Schedule P of the annual statements mandated by the NAIC. We explore the relative size of each of these lines of business and trends in line of business size over time. We also look at the degree of market concentration within each line of business, and the extent to which insurers diversify their activities across multiple lines of business.
#level-beginner #industry-analysis #featured
Casualty Insurance Industry Overview

Line of Business Development Patterns

When an insurance company issues a policy, the company knows the amount of premium it will receive, but it may not know for many years exactly how much it will cost to settle all of the claims associated with that policy. The study of patterns of claims emergence and loss payments is called loss development. We illustrate a few of the key characteristics of loss development and how it varies by statutory line of business and by company. Finally, we look at the relationship between the length of time it take for losses to develop and the degree of uncertainty surrounding the ultimate value of those losses.
#industry-analysis #level-beginner #featured
Casualty Insurance Industry Overview

Line of Business Loss Ratio Behavior

The core measure of an insurance company's performance is its loss ratio. We describe what loss ratios are, and how they tend to behave. We explore how loss ratios vary by line of business, and what types of variation in behavior are typical. Finally, we explore the root causes behind why different lines of business have different loss ratio behavioral characteristics.
#industry-analysis #level-intermediate #featured

Modeling Philosophy

Overview of Ledger's Modeling

Ledger's Modeling Philosophy

Ledger Investing does not use actuarial science to price risk. We explain why we don't, and provide an intuitive justification of our alternate method through an analogy to a fund of funds.
#level-beginner #philosophy
Overview of Ledger's Modeling

Ledger's Loss Forecasting Strategy

Ledger uses a strategy for forecasting casualty insurance loss ratios that is significantly different from traditional actuarial practice. We describe how Ledger's analytics team approaches this problem, how our approach differs from traditional methods, and the justification behind our approach.
#philosophy #level-beginner #featured
Overview of Ledger's Modeling

Blurry Images and Hierarchical Models

We share a series of blurry images and ask you, the reader, to make some predictions about those pictures. We then use this series of examples to illustrate the power and value of hierarchical modeling.
#featured #level-beginner #philosophy

Anthologies

new-york-skyline
Anthologies

Property and Casualty Insurance Industry Analysis

This anthology is a collection of articles we've written on the property and casualty insurance industry. It covers basics of the property and casualty insurance space, analyses of the competitive landscape, describes differences between lines of business, and explores possible causal explanations for these differences. The anthology includes the following articles published individually: - Property & Casualty Insurance Companies - Property & Casualty Lines of Business - Line of Business Volume and Diversification - Line of Business Development Patterns - Line of Business Loss Ratio Behavior
#anthology

Preprints

Tail Factor Models

Improved Estimation of Parametric Tail Factor Models

Loss development tail factors are difficult to estimate, due to training data that is typically quite sparse and volatile. We propose a new estimation technique that is well-grounded in statistical theory, applicable to a broad class of tail factor methods, and relatively easy to implement. We demonstrate its superior performance compared to other extant estimation techniques.
#preprint #technical #level-advanced
Tail Factor Models

A Power Transform Generalization of Parametric Tail Factor Methods

Many tail factor estimation methods in common usage revolve around fitting a parametric curve to age-to-age factors or link ratios. In this paper, we propose a new parametric curve for this purpose. We demonstrate that two popular tail curve forms (the exponential decay method and Sherman’s method) can be obtained as special cases of this general form. We also show that, given appropriate priors on its parameters, the new model can achieve superior predictive performance.
#preprint #technical #level-advanced
Loss Modeling Software

BayesBlend: Easy Model Blending using Pseudo-Bayesian Model Averaging and Stacking in Python

Averaging predictions from multiple candidate inferential models frequently outperforms predictions from any given candidate model in isolation. Here, we introduce BayesBlend, the first all-in-one software library that estimates weights and blends multiple (Bayesian) models' predictive distributions. BayesBlend implements pseudo-Bayesian model averaging, stacking, and hierarchical Bayesian stacking to estimate model weights. We include real-world examples using BayesBlend in the context of loss ratio development and loss ratio forecasting.
#preprint #technical #level-advanced
Overview of Ledger's Modeling

A Bayesian workflow for securitizing casualty insurance risk

In this paper, we lay out our Bayesian workflow for securitizing casualty insurance-linked securities that uses: (1) theoretically informed time-series and state-space models to capture how loss ratios develop and change over time; (2) historic industry data to inform prior distributions of models fit to individual programs; (3) stacking to combine loss ratio predictions from candidate models, and (4) both prior predictive simulations and simulation-based calibration to aid model specification. Using historic Schedule P filings, we then show how our proposed Bayesian workflow can be used to assess and compare models across a variety of key model performance metrics evaluated on future accident year losses.
#preprint #technical #level-advanced