Excel continues to be actuaries’ most widely used software tool, with more than
94.3% of respondents reporting that they use it at least once a day.
• With that understood, most actuaries (92.3%) use more than one tool.
• Actuaries want to increase their proficiency in R (47.2%), Python (39.1%), SQL
(30.8%), and Excel (26.0%).
• No tool had more than 50% of respondents indicating that they wanted to increase
their proficiency.
• Time is the greatest barrier to learning new technology. (80.5% of respondents felt
• Newer analysis methods such as tree-based algorithms and artificial intelligence (AI)
are not widely used (16.5% and 7.0%, respectively).

Author(s): Casualty Actuarial Society

Publication Date: March 2022

Publication Site: CAS Research Paper

2021 Academy Legislative/Regulatory Review



The American Academy of Actuaries presents this summary of select significant regulatory and
legislative developments in 2021 at the state, federal, and international levels of interest to the U.S.
actuarial profession as a service to its members.


The Academy focused on key policy debates in 2021 regarding pensions and retirement, health, life,
and property and casualty insurance, and risk management and financial reporting.

Responding to the COVID-19 pandemic, addressing ever-changing cyber risk concerns, and analyzing
the implications and actuarial impacts of data science modeling continued to be a focus in 2021.

Practice councils monitored and responded to numerous legislative developments at the state, federal,
and international level. The Academy also increased its focus on the varied impacts of climate risk and
public policy initiatives related to racial equity and unfair discrimination in 2021.

The Academy continues to track the progress of legislative and regulatory developments on actuarially
relevant issues that have carried over into the 2022 calendar year.

Publication Date: 15 Feb 2022

Publication Site: American Academy of Actuaries

Thomas Bond Sprague (1830-1920)




Dr Sprague was the main person behind a mortality study covering the experience of twenty U. K. life offices. This study resulted in the Institute of Actuaries Life Tables (the so-called Twenty Offices Table) which was published in 1869 [2]. From this study, he produced, in 1879, the first Select Tables of Mortality [3] which were the first two-dimensional mortality tables ever published (the two dimensions being ‘insured duration’ i.e. the ‘select period’ and ‘age attained’). The ‘select period’ was five years.

Dr Sprague pioneered the important 1870 Life Insurance Companies Act [4] which was introduced following the notorious insolvencies of both the Albert and the European life assurance companies. The 1870 Act required:-

… an investigation into the financial condition of a life insurance company to be made regularly by an actuary,

required a separate “long-term fund” and required the:-

… preparation of a revenue account and balance sheet every year in prescribed form to be filed with the Board of Trade,

the latter being a public document. Dr Sprague was one of the foremost advocates of the principle of ‘Freedom with Publicity’ (i.e. documents available to the public) and was opposed to there being any Government regulation prescribing the manner of valuation of policy liabilities. He wrote the major 19th century work on the preparation of life office accounts in conformity with the 1870 Act [5].

Author(s): David O Forfar

Publication Date: accessed 9 Feb 2022

Publication Site: MacTutor History of Math Archives

USQS Roundtable—All About the Amended Standards



TC: The work of the actuary is evolving more and more toward big data and artificial intelligence. In addition, we are seeing evolving regulatory and societal requirements that will place new demands on the actuary’s work. These new areas involve working with more unknowns in the tools actuaries use—such as data, models, algorithms, and assumptions. In order to be effective in these new areas, and to continue to earn the public’s trust in our work, we need to better understand what can impact the appropriateness and effectiveness of these tools. As these areas evolve, it is important for actuaries to understand the potential limits of these tools. This is where obtaining continuing education on bias topics can help. As the USQS lay out, bias topics may include “content that provides knowledge and perspective that assist in identifying and assessing biases that may exist in data, assumptions, algorithms, and models that impact Actuarial Services. Biases may include but are not limited to statistical, cognitive, and social biases.” This is a broad topic, but I believe it will better equip the actuary in our role of maintaining the public’s trust in insurance and pension systems.

LS: Indeed, bias topics are broad. When performing actuarial services there are so many ways that bias impacts our work that we need to keep the topic broad in order that the range of continuing education will give us the appropriate tools. The obvious ways that bias may impact our work are in selection of data, as well as designing, developing, selecting, modifying, or using all types of models and algorithms. Even more important is how we communicate the results of our work. We also operate in a world where we can individually be blindsided by biases that we bring to our work and impact the transparency and validity of the actuarial services that we are providing. Because of our basic education, we know what bias is. That is something that we can continue to fine-tune and will have significant benefits to the reputation of actuaries and allow us to further differentiate our professionalism compared with others, particularly many data scientists.

Publication Date: Jan/Feb 2022

Publication Site: Contingencies

Getting Started with Julia for Actuaries




Sensitivity testing is very common in actuarial workflows: essentially, it’s understanding the change in one variable in relation to another. In other words, the derivative!

Julia has unique capabilities where almost across the entire language and ecosystem, you can take the derivative of entire functions or scripts. For example, the following is real Julia code to automatically calculate the sensitivity of the ending account value with respect to the inputs:

When executing the code above, Julia isn’t just adding a small amount and calculating the finite difference. Differentiation is applied to entire programs through extensive use of basic derivatives and the chain rule. Automatic differentiation, has uses in optimization, machine learning, sensitivity testing, and risk analysis. You can read more about Julia’s autodiff ecosystem here.

Author(s): Alec Loudenback, FSA, MAAA; Dimitar Vanguelov

Publication Date: October 2021

Publication Site: SOA Digital, Emerging Topics



doi: : 10.2478/v10127-012-0025



In life insurance mathematics, the concept of a survival function is commonly
used in life expectancy calculations. The survival function of a random variable X
is defined at x as the probability that X is greater than a specific value x. For
a non-negative random variable whose expected value exists, the expected value
equals the integral of the survival function. We propose to designate this result
as the Darth Vader Rule1. It holds for any type of random variable, although its
most general form relies on the integration by parts formula for the Lebesgue-
-Stieltjes integral, fully developed by H e w i t t [3]. This result, while known (and
stated in F e l l e r [1]), is not widely disseminated except in life insurance mathematics texts; but it is worth knowing and popularizing because it provides an
efficient tool for calculation of expected value, and gives insight into a property
common to all types of random variables.
We give a proof of the Darth Vader Rule which works for all random variables which are non-negative almost surely and whose expected value exists.
The proof is based not on the Lebesgue integral formulation of [3], but on the
generalized Riemann integration of H e n s t o c k and K u r z w e i l [2], [4]. Since
every Lebesgue integrable function is also generalized Riemann integrable, the
proof here includes all cases covered by [3].
While the result is simple to state and comprehend, its proof using Lebesgue
integral theory is somewhat complex.

Author(s): Pat Muldowney — Krzysztof Ostaszewski — Wojciech Wojdowski

Publication Date: 2012

Publication Site: Tatra Mountains Mathematical Publications

Mortality Nuggets: Videos on 2020 Death Rates by Cause of Death, Querying WONDER, and Actuarial News




Actuarial News is a website Stu created for me to use as a place to collect all the articles, websites, data sources, etc. that I like to use for my research and writing. I tend to develop ideas over long periods, and I prefer my selections over trying to use regular search.

As noted in the video, I used to use the old Actuarial Outpost (RIP) as a repository for my articles on public pensions and finance, but now I use Actuarial.News.

By the way, for any readers seeking actuarial discussion as once was provided by the old Outpost, check out goActuary. I have a thread on spreadsheet screwups and one on non-pandemic mortality, for instance.

Author(s): Mary Pat Campbell

Publication Date: 25 Jan 2022

Publication Site: STUMP at substack

Insurance Companies – Heels or Heroes?



The insurance industry is far from the economy’s most-admired sector. A Forbes survey found insurance ranking low in popularity in the public eye. Three main reasons are responsible for insurers’ relatively poor rating. First is the intangible nature of the insurance product. Unlike a car one can drive home from the dealership, or a chocolate bar whose taste can be savored, purchase of an insurance policy does not lead to immediate physical gratification. To be sure, if there is no loss, one may never get a flavor of its value. Second, insurance is associated with life’s tragedies, its most physically, emotionally and financially distressing experiences—a home damaged by a storm, a car totaled, being sued, a death or dread disease, or a crippling workplace accident. Insurance payments can take away the sting with financial recovery, but loss remains painful, especially if one discovers the loss is not 100 percent covered. And third, the insurance industry has become an easy target for critics who regularly vilify it.


Why do we maintain that insurance, R Street’s inaugural research program, is fundamentally exciting? Three reasons.

First, insurance is the economy’s financial first responder. When the wind blows, the earth shakes and large-class action lawsuits are decided in plaintiffs’ favor, the insurance industry pays. 


Second, insurers are significant investors in the capital markets. They provide much of the financial muscle to power the economy. Property-casualty insurers hold $1.1 trillion in bonds, and life and health insurers hold another $3.6 trillion. Collectively, insurers hold $4.7 trillion in bonds, 10 percent of the U.S. bond market of $47 trillion.


Third, insurance is the grease in the engine of the economy. Without clinical trials insurance, pharmaceutical companies would not take the risk of developing vaccines. Without ocean marine or inland marine insurance, ships would not sail and trucks would not take the risk to carry loads. Airplanes would not fly, people would be afraid to drive, and inventors would not create new products for fear of lawsuits. 

Author(s): Jerry Theodorou

Publication Date: 22 Jan 2022

Publication Site: R Street

Actuarial Data Science Tutorials




On this page we present all the tutorials that have been prepared by the working party. We are intensively working on additional ones and we aim to have approx. 10 tutorials, covering a wide range of Data Science topics relevant for actuaries.

All tutorials consist of an article and the corresponding code. In the article, we describe the methodology and the statistical model. By providing you with the code you can easily replicate the analysis performed and test it on your own data.

Author(s): Swiss Association of Actuaries

Publication Date: accessed 20 Jan 2022

Publication Site: Actuarial Data Science

Want to Be an Actuary? Odds Are, You’ll Fail the Test



(the answer: B — I’ll leave it to you to verify the calculations)


Actuaries quantify risk. One of their riskiest endeavors is trying to become one.

Among people taking at least one exam from the Society of Actuaries—the field’s biggest U.S. credentialing body—15% eventually pass the multiple tests required to become an Associate, one of two designations allowing them to practice. Just 10% pass those and additional tests to become a Fellow, the group’s higher designation, which affords bigger responsibilities and salaries.

It’s such an arduous process that the number of test-takers has been declining in recent years, and the society is making changes to keep candidates from dropping out of the gantlet. It is also adding new “predictive analytics” tests to adjust to the massive amounts of data insurers now have.

There is no limit to how many times a candidate can take the tests. It took one man 50 years to become a Fellow, says Stuart Klugman, an official at the society. The society says a candidate typically takes seven to 10 years to become a Fellow. They must pass 10 exams plus other coursework and requirements.

Author(s): Neal Templin

Publication Date: 28 Dec 2021

Publication Site: WSJ

Emerging Technologies and their Impact on Actuarial Science




This research evaluates the current state and future outlook of emerging technologies on the actuarial profession
over a three-year horizon. For the purpose of this report, a technology is considered to be a practical application of
knowledge (as opposed to a specific vendor) and is considered emerging when the use of the particular technology
is not already widespread across the actuarial profession. This report looks to evaluate prospective tools that
actuaries can use across all aspects and domains of work spanning Life and Annuities, Health, P&C, and Pensions in
relation to insurance risk.
We researched and grouped similar technologies together for ease of reading and understanding. As a result, we
identified the six following technology groups:

  1. Machine Learning and Artificial Intelligence
  2. Business Intelligence Tools and Report Generators
  3. Extract-Transform-Load (ETL) / Data Integration and Low-Code Automation Platforms
  4. Collaboration and Connected Data
  5. Data Governance and Sharing
  6. Digital Process Discovery (Process Mining / Task Mining)


Nicole Cervi, Deloitte
Arthur da Silva, FSA, ACIA, Deloitte
Paul Downes, FIA, FCIA, Deloitte
Marwah Khalid, Deloitte
Chenyi Liu, Deloitte
Prakash Rajgopal, Deloitte
Jean-Yves Rioux, FSA, CERA, FCIA, Deloitte
Thomas Smith, Deloitte
Yvonne Zhang, FSA, FCIA, Deloitte

Publication Date: October 2021

Publication Site: Society of Actuaries, SOA Research Institute

Annual Report on the Insurance Industry




Catastrophe losses of $61 billion in 2020 were notably more severe than in 2019, with a record number of
catastrophic events in the United States in 2020.46 Despite the more severe catastrophic event
losses, lower losses in personal and commercial auto and workers’ compensation lines kept total
loss and loss adjustment expenses flat from 2019 to 2020. Reserve development was again
favorable in 2020, adding to underwriting profits. Figure 24 shows losses from catastrophic
events in the United States since 2016, and Figure 25 shows reserve development over the same
period.47 The expense ratio decreased very slightly from 2019 to 2020.

Publication Date: September 2021

Publication Site: Federal Insurance Office