Actuarial Science in Mexico

The science that brings certainty
to uncertainty

The Spanish-speaking world's meeting point for the actuarial profession: history, the mathematics of risk, formulas, careers and the institutions shaping Mexico's financial future.

Explore the lab See actuarial formulas
1947
A pioneer in Latin America
+20
Universities in Mexico
#1
In graduate employment
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What's new

New tools for the actuary

Simulators, official data, worked problems and guides on the risks that occupy the profession today, all with verified sources.

InitiativeJoin the actuaries community on WhatsAppTopic groups for students and practitioners: questions, events, calls and job openings. Request your invitation.NewIMSS pension simulatorLey 73, Ley 97, Modalidad 40 (voluntary continuation) and a longevity illustrator built on EMSSA tables.NewProblem bank64 worked problems and an exam simulator for CNSF, CONAC and SOA.NewTables and dataUMA, minimum wage, INPC, UDI, interest rates and life expectancy in CSV.NewRegulatory monitorCUSF and CONSAR circulars, NIF and international standards, kept up to date.NewClimate and sustainabilityClimate risk, scenarios and a proposed actuarial climate index.NewMexico in numbersInsurance, pensions and demographics on one dashboard with official sources.NewPublic policyTechnical notes on pensions, the IMSS liability and the protection gap.NewActuarial work in R and PythonPackages, executed recipes and good modeling practice.
Actuarial Lab · Interactive

Play with risk and life

A live Gompertz mortality model. Move the age and the interest rate and watch how the survival curve and the value of a life annuity change: the core of pension and life insurance calculations.

Survival curve $\ell_x$

Projected survivors from the selected age.
Illustrative Gompertz model: $\mu_x = B\,c^{\,x}$. It does not replace a regulatory mortality table (EMSSA / CNSF).

Life annuity and life insurance

Actuarial present value computed in real time.
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Annuity $\ddot{a}_x$
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Insurance $A_x$
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Life exp. $e_x$
$$\ddot{a}_x=\sum_{k=0}^{\infty} v^{k}\,{_k p_x}\qquad A_x = 1 - d\,\ddot{a}_x$$

More interactive calculators

From property and casualty insurance to investments: move the controls and watch how risk changes the outcome.

P&C insurance: risk premium

Collective risk model: frequency × severity plus a risk loading.
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Pure premium
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Std. dev. σ
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Loaded premium
Compound Poisson: $E[S]=\lambda\mu$, $\sigma_S=\mu\sqrt{2\lambda}$. Premium $=E[S]+\theta\,\sigma_S$.

Investments: risk and return

Two-asset portfolio (Markowitz). Equities 9%/18%, bonds 4%/6%.
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Exp. return
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Volatility
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Sharpe
$\sigma_p=\sqrt{w^2\sigma_a^2+(1-w)^2\sigma_b^2+2w(1-w)\rho\sigma_a\sigma_b}$. Risk-free rate 3%.

Investment: projection under risk

Lognormal growth with a P5 to P95 uncertainty band.
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Expected value
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P5 (bad)
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P95 (good)
$V_T=V_0\,e^{(\mu-\sigma^2/2)T\,\pm\,z\,\sigma\sqrt{T}}$, with $z_{95}=1.645$.
Timeline

History of the actuarial profession in Mexico

From the first colonial insurance arrangements to the modern financial system: centuries of actuarial development in Mexico.

1789
Monte de Piedad: the first actuarial foundations
The Nacional Monte de Piedad lays the groundwork for risk and reserve calculations in Mexico, bringing proto-actuarial concepts into its pawn lending operations.
1892
The first formal insurance companies
The first insurers with structured operations are established in Mexico, importing European actuarial methods to value life and accident policies.
1929
Ley General de Instituciones de Seguros (General Insurance Institutions Law)
The Mexican state formally regulates the insurance market, requiring technical reserves and actuarial studies. The official need for actuaries in the national financial system is born.
1946 and 1947
The first bachelor's degree in Actuarial Science (UNAM)
In 1946 the Instituto Mexicano de Actuarios proposed to UNAM that it create the degree; the first curriculum was approved on February 13, 1947 at the Facultad de Ciencias. It is the first bachelor's degree in Actuarial Science in Latin America.
1962 · 1966
The actuarial profession organizes
In 1962 the Asociación Mexicana de Actuarios (AMA) was founded. In 1966 the Colegio de Actuarios de México, A.C. was established; in 1982 it adopted the name Colegio Nacional de Actuarios (CONAC), promoting ethics and technical standards in the profession.
1990s
Expansion into pensions and finance
Economic liberalization and the reform of the Sistema de Ahorro para el Retiro (SAR, the retirement savings system, with the Afores in 1997) drive demand for actuaries specialized in pensions, investments and financial risk management.
Today
The era of data and quantitative risk
Modern actuaries combine data science, machine learning and advanced stochastic modeling to solve risk problems in sectors as diverse as banking, health, energy and cybersecurity.
The Profession

What is Actuarial Science?

The discipline that applies mathematics, statistics and financial theory to assess risk in insurance, pensions, investments and finance.

The Mathematics of Risk

Actuaries use probability, ruin theory, stochastic models and statistics to quantify uncertain events and their financial consequences.

Professional Practice

They design insurance products, calculate technical reserves, value pension funds, structure investment portfolios and advise on enterprise risk management.

Science and Innovation

Today actuarial science works alongside data science, artificial intelligence and advanced computational modeling to solve complex problems in modern finance.

Regulatory Framework

Actuaries ensure that financial institutions meet the legal and prudential requirements set by the CNSF (National Insurance and Surety Commission), CONSAR (National Retirement Savings Commission) and Banco de México.

Global Reach

The actuarial profession is recognized internationally. Mexican actuaries take part in bodies such as the IAA (International Actuarial Association) and collaborate worldwide.

Data and Analytics

With the rise of big data, actuaries lead predictive analytics in health, cybersecurity, climate change and asset management.

Professional Development

The actuarial career

From the bachelor's degree to international credentials: a demanding path, and an exceptionally rewarding one.

Academic Training

The bachelor's degree in Actuarial Science is taught at UNAM, ITAM, Anáhuac, UDLA and other institutions. The curriculum covers mathematics, statistics, economics, finance and computer science.

CONAC Certifications

The Colegio Nacional de Actuarios issues professional certifications that attest to technical competence in areas such as insurance, pensions, finance and investments.

International Exams

Many Mexican actuaries earn the prestigious Fellow of the Society of Actuaries (FSA) or Fellow of the Casualty Actuarial Society (FCAS) credentials, or the IAA's CERA.

Where Actuaries Work

Life and P&C insurance, pensions and Afores, banking, consulting, the federal government (CNSF, CONSAR, SHCP), investment funds and fintech companies.

Pay and Outlook

Actuaries consistently rank among the best-paid professionals in Mexico. Demand exceeds the supply of graduates, creating excellent job opportunities.

Actuarial Science and Technology

Combining actuarial thinking with programming in Python, R and SQL, plus machine learning, makes the modern actuary a highly competitive profile.

Mexico by the Numbers

The profession in figures

1947
First Actuarial Science curriculum (UNAM), a pioneer in Latin America
+20
Universities offering the degree in Mexico
#1
Actuarial Science ranks among the degrees with the highest graduate employment
Institutions

Associations and institutions

The Mexican actuarial ecosystem rests on professional bodies, regulators and leading international organizations.

CONAC

Colegio Nacional de Actuarios

The professional body that certifies, brings together and promotes ethical and technical standards for actuaries in Mexico.

CNSF

Insurance and Surety

Comisión Nacional de Seguros y Fianzas (National Insurance and Surety Commission). It regulates and supervises the insurance sector, where actuaries are key figures in regulatory compliance.

CONSAR

Retirement Savings

It supervises the Afores and the pension system, where actuarial science is essential to valuing liabilities.

IAA

International Actuarial Association

The worldwide federation of actuarial associations. Mexico takes an active part through CONAC as a full member.

SOA

Society of Actuaries

The US organization that grants the FSA and CERA credentials, widely held by Mexican actuaries in life and health.

CAS

Casualty Actuarial Society

Specialized in property and casualty insurance and liability. Its exams and the FCAS credential are valued in the Mexican market.

See all institutions
★ Special Section
Colegio Nacional de Actuarios

CONAC, your professional body

The organization that has brought together, represented and certified actuaries in Mexico since 1966.

Who we are

The Colegio Nacional de Actuarios (CONAC) is a civil association established on November 16, 1966 (originally as Colegio de Actuarios de México, A.C.) that brings together the actuaries of Mexico. It adopted its current name in 1982. It is one of the bodies that represent the actuarial profession before government, the financial sector and international organizations.

CONAC is a full member of the International Actuarial Association (IAA), which ensures that its technical and ethical standards are aligned with global best practice.

Founded

1966. More than half a century representing the actuarial profession in Mexico.

IAA Member

Part of the International Actuarial Association as a full member.

Current name

Adopted the name Colegio Nacional de Actuarios in 1982.

Headquarters

Mexico City, with a presence across the country.

Mission and Vision

Mission: To promote the comprehensive development of the actuarial profession in Mexico through professional certification, continuing education, advocacy for the interests of its members and active participation in the national and international financial and regulatory environment.

Vision: To be the undisputed benchmark of actuarial excellence in Mexico and Latin America, developing actuaries who lead the transformation of the financial system with technical rigor, ethical integrity and vision.

  • Set and promote ethical and actuarial practice standards
  • Represent Mexico before international actuarial organizations
  • Foster continuing education and professional development
  • Work with regulators on the design of technical regulation
  • Promote actuarial research applied to the Mexican context

Member Services

CONAC offers its members a broad range of services to support their professional development and keep them at the forefront of actuarial knowledge:

  • Continuing education programs and specialized courses
  • National and international actuarial congresses and symposia
  • Technical publications and a digital actuarial library
  • A network of actuaries across Mexico and around the world
  • Guidance on ethics and professional practice
  • Access to the International Standards of Actuarial Practice (ISAP)
  • Representation of the profession before regulatory authorities
  • A public directory of certified actuaries

Professional Certification

CONAC certification is the hallmark of technical excellence for actuaries in Mexico. It attests that the professional meets the highest standards of actuarial competence and ethics.

Life and Health

Certification in life insurance, medical expense and employee benefit products.

Pensions

Specialization in pension funds, retirement plans and social security systems.

Property and Casualty

Property and casualty insurance, liability, reinsurance and catastrophe risk underwriting.

Finance

Asset management, quantitative financial risk, derivatives and capital markets.

To obtain certification, an actuary must meet professional experience requirements, pass technical exams and commit to continuing education and the CONAC Code of Ethics.

Contact and Official Website

For official information, membership procedures, certification and events, visit the official CONAC website:

Website

conacmexico.org.mx

Headquarters

Mexico City, Mexico.

Events

See the calendar of courses, congresses and webinars on the official portal.

Membership

Admission and renewal procedures are available online through the CONAC portal.

For future actuaries

Thinking about studying Actuarial Science?

Everything a student needs to decide and get started: why it is worth it, what you study and where the profession comes from.

Why study Actuarial Science?

One of the best professions in the world: mathematics plus business, strong pay, high demand and 22% growth.

Find out

Syllabus and exams

What associations and universities require: the IAA core syllabus, SOA and CAS exams, VEE and CONAC certification.

See the syllabus

History of the profession

From Pascal and Halley to modern risk theory, and the history of the profession in Mexico since the 19th century.

Read the history
See the universities that offer it
Go deeper

Actuarial concepts

Pages devoted to the major topics of actuarial science, with theory, formulas, worked examples and interactive calculators. See also the 16 actuarial specialties or the full topic library.

Pensions

Life annuities, projected unit credit, pension liabilities and the Mexican system (IMSS, AFORE, Modalidad 40).

Explore

Credibility

How to blend individual and collective experience: classical, Bühlmann and Bayesian credibility.

Explore

Loss Functions

Loss distributions, risk measures (VaR, TVaR) and loss functions in estimation and pricing.

Explore

Reinsurance

Proportional and non-proportional: quota share, surplus, excess of loss, stop-loss and optimal retention.

Explore

Universities

A verified directory of the public and private universities that teach Actuarial Science in Mexico.

Explore

Famous actuaries

From Halley to Bühlmann, plus the figures and milestones of Mexican actuarial science: who shaped the profession.

Explore

Actuar.IA · Actuarial Science and AI

Statistical foundations, machine learning and neural networks applied to risk, with references from the SOA and the CAS.

Explore

Mortality tables and longevity

Biometric functions, Gompertz and Makeham, period and generational tables, Lee-Carter, EMSSA and CNSF tables and the measurement of longevity risk.

Guide and calculator

Insurance pricing

Pure premium, loadings and gross premium, the pure premium and loss ratio methods, trend, GLMs and relativities, credibility and rate adequacy under the LISF (Insurance and Surety Institutions Law).

Guide and calculator

Technical reserves

Unearned premium, outstanding claims, IBNR with chain-ladder, Bornhuetter-Ferguson, Cape Cod, Mack and bootstrap, best estimate and risk margin under the LISF and CUSF (Single Insurance and Surety Circular).

Guide and calculator

Risk and ruin theory

The Cramér-Lundberg process, safety loading, adjustment coefficient, Lundberg's inequality, the exact exponential formula, the collective model, Panjer, approximations and reinsurance.

Guide and calculator

Insurance solvency and capital

Solvency capital requirement (RCS) at a one-year 99.5% VaR, eligible own funds, the investment base, dynamic solvency testing and the ARSI (own risk and solvency assessment): the LISF regime compared with Solvency II.

Guide and calculator

IFRS 17 Insurance Contracts

General model, VFA and PAA; contractual service margin, risk adjustment, onerous contracts and transition, with a CSM example and the status of the standard in Mexico.

Guide and calculator

Catastrophe risk and climate change

Hazard, vulnerability and financial modules; PML, AEP, OEP and return periods; the CNSF's Sistema R and RH-Mex, the catastrophe reserve, cat bonds, parametric insurance and climate scenarios.

Guide and calculator

Employee benefits: NIF D-3 and IAS 19

Seniority premium, statutory severance and pension plans valued with projected unit credit: DBO, service cost, interest cost, remeasurements and the differences between NIF D-3 and IAS 19.

Guide and calculator
Notation and Mathematics

Actuarial formulas

The main formulas and notation of actuarial science, from life insurance mathematics to reserving models and risk theory.

Survival Probability

Probability of surviving t years

$$_tp_x = \frac{\ell_{x+t}}{\ell_x}$$

Probability that a person aged $x$ survives at least $t$ more years. $\ell_x$ is the number of lives at age $x$ in the mortality table.

Death Probability

Probability of dying within t years

$$_tq_x = 1 - {_tp_x} = \frac{\ell_x - \ell_{x+t}}{\ell_x}$$

Probability that a person aged $x$ dies within the next $t$ years. For $t=1$ it is written simply $q_x$.

Life Expectancy

Curtate expectation of life

$$e_x = \sum_{k=1}^{\infty} {_kp_x}$$

Expected number of complete future years lived by a person aged $x$. It is the sum of the probabilities of surviving at least $k$ years.

Actuarial Present Value

Whole life insurance (payable at death)

$$A_x = \sum_{k=0}^{\infty} v^{k+1} \cdot {_kp_x} \cdot q_{x+k}$$

Actuarial present value of an insurance paying $1$ unit at the end of the year of death. $v = \frac{1}{1+i}$ is the discount factor.

Life Annuity

Whole life annuity-due

$$\ddot{a}_x = \sum_{k=0}^{\infty} v^k \cdot {_kp_x}$$

Present value of an annuity paying $1$ unit at the start of each year while the insured aged $x$ remains alive. It is the basis of pension calculations.

Fundamental Relationship

Insurance-annuity identity

$$A_x = 1 - d \cdot \ddot{a}_x$$

The fundamental relationship between whole life insurance and the whole life annuity-due, where $d = \frac{i}{1+i}$ is the rate of discount. Essential for premium calculation.

Net Premium

Level annual net premium

$$P(A_x) = \frac{A_x}{\ddot{a}_x}$$

Annual net premium that equates the present value of benefits with the present value of future premiums. The actuarial equivalence principle.

Policy Reserve

Prospective reserve at time t

$${_tV}(A_x) = A_{x+t} - P(A_x)\cdot\ddot{a}_{x+t}$$

Value of the insurer's net future obligation at time $t$: the PV of future benefits minus the PV of future premiums. Required by regulation.

Risk Theory

Aggregate loss distribution (Panjer)

$$f_S(x) = \frac{1}{x}\sum_{y=1}^{x}(a + by)\, f_Y(y)\, f_S(x-y)$$

Panjer recursion to compute the distribution of aggregate losses $S = Y_1 + \cdots + Y_N$, when $N$ belongs to the $(a,b,0)$ class (Poisson, binomial, negative binomial).

Ruin Theory

Probability of ruin (Cramér-Lundberg)

$$\psi(u) \leq e^{-Ru}$$

Upper bound on the probability of ruin for initial capital $u$, where $R$ is the adjustment coefficient satisfying Lundberg's equation: $\lambda + cR = \lambda M_Y(R)$.

Pensions

Pension liability (projected unit credit)

$$\text{BO}_t = \frac{n_t}{N} \cdot \text{SP}_N \cdot \ddot{a}_{r}$$

Accrued benefit obligation at year $t$: the proportion of service rendered ($n_t/N$) times projected salary at retirement ($\text{SP}_N$) times the present value of the annuity at retirement ($\ddot{a}_r$).

Interest and Discount

Life annuity deferred n years

$$_{n|}\ddot{a}_x = v^n \cdot {_np_x} \cdot \ddot{a}_{x+n}$$

Annuity deferred $n$ years: payments begin in $n$ years if the insured survives. It combines financial discounting $v^n$ with the survival probability ${_np_x}$.

Guide to Standard Actuarial Notation

SymbolNameDescription
$x$Age of the insuredCurrent age of the person under study
$t$Time / TermNumber of years elapsed or length of the period
$\ell_x$Lives at age xNumber of survivors at age $x$ in the mortality table
$d_x$Deaths between x and x+1$d_x = \ell_x - \ell_{x+1}$
$q_x$Probability of deathProbability of dying between ages $x$ and $x+1$
$p_x$Probability of survivalProbability of surviving from age $x$ to $x+1$
$_tp_x$Prob. of surviving t yearsProbability of surviving $t$ years from age $x$
$e_x$Curtate life expectancyExpected number of complete future years
$\mathring{e}_x$Complete life expectancyTotal expected future years (including fractional years)
$v$Discount factor$v = (1+i)^{-1}$, where $i$ is the annual interest rate
$d$Rate of discount$d = iv = i/(1+i)$
$A_x$Whole life insuranceAPV of an insurance paying at the end of the year of death
$\ddot{a}_x$Whole life annuity-dueAPV of annual payments at the start of each period while alive
$a_x$Whole life annuity-immediateAPV of annual payments at the end of each period while alive
$P(A_x)$Level net premiumAnnual premium that balances benefits and premiums under the equivalence principle
$_tV$Policy reserveInsurer's prospective net liability at time $t$
$\mu_x$Force of mortalityInstantaneous rate of mortality at age $x$
$\delta$Force of interest$\delta = \ln(1+i)$, the instantaneous rate of interest

Explore actuarial science from start to finish

From the definition and history to pensions, reinsurance, credibility and the universities that train Mexico's actuaries. All in one place.

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About the Author

Who is behind this site

Act. Frank Ruiz de la Peña Olea
★ Certified Actuary
Act. Frank Ruiz de la Peña Olea
Actuary · Specialist in Actuarial Science

This site was created and is maintained by Act. Frank Ruiz de la Peña Olea, a Mexican actuary trained in insurance mathematics, risk theory, investments and actuarial finance. Its mission is to share actuarial knowledge in Spanish, bring actuarial science closer to the general public and support students and practitioners of the profession in Mexico and Latin America.

Into actuaria.mx he has poured everything he knows about the actuarial profession. His active involvement in actuarial organizations in Mexico and around the world, and his attendance at international congresses and events of the profession, have given him a global view of actuarial science that is reflected in every section of this portal.

Certified before CONSAR Actuary accredited by the CNSF
Insurance Mathematics Risk Theory Pensions Reinsurance Investments Actuarial Finance CNSF
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«My goal with this portal is to share and promote the actuarial profession in Mexico, bring it closer to new generations and contribute, as far as I can, to strengthening and elevating the Mexican actuarial community.»

This site grew out of a conviction: that the actuarial profession in Mexico deserves to be better known and held in higher esteem. Throughout my career I have gathered material on actuarial science, its history, its technical foundations, its institutions, its regulation and its place in the world, and actuaria.mx is the result of organizing all of it in one clear, accessible place for students, prospective students, practitioners and anyone interested.

What you will find here

SpecialtiesThe 16 fields of actuarial practice Actuar.IAActuarial science and artificial intelligence HistoryWhere the profession comes from FormulasThe mathematics of risk UniversitiesWhere to study Actuarial Science BooksThe essential library