Areas of Application

In Mexico, actuaries have entered a wide area of very diverse application, since not only individuals are exposed to different kinds of risks, but enterprises and society also live in situations of uncertainty. This, linked to the mathematical rigor that the career gained from being founded in the Mathematics Department of the Faculty of Sciences of the UNAM, actuary in Mexico has been granted a signature trait: its multidisciplinary or multifaceted character. Mexican actuaries, mainly after the seventies, started to venture into areas that are not common in other countries, like statistics, probability, demographics, informatics and operations investigation, among others.

The areas in which a career graduate can work are very diverse, since these are not really branches of actuarial studies, but actuary is an instrument with potential to contribute solutions into many fields.


Demography is the scientific study of human population. An important part of these studies is constituted my demographical projections.

This labor is very important, since it allows planning, but for public decision making it is necessary to have a notion of demographical conditions, for example, to be able to develop plans as a society. That is why actuarial estimations aim to provide a general idea about a population’s behavior, which is recalibrated according to how certain situations unfold.


For practical purposes, we can classify an extense list of insurances that may be acquired in the market into two groups: life insurance and the rest.

Life Insurance

A life insurance aims to compensate the loss of income that, if alive, a person would generate. The actuary is in charge of calculating a prime, this prime is paid by many clients who wish to acquire an insurance, that quantity should be enough to cover for the deceased, cover for administrative costs and gain a pfofit.

Non-life insurances

We refer to those risks associated with an event that, were it to happen, would cause a loss that can be quantified.

This covers a great amount of insurance, all those losses that can be quantified and have a maximum amount (fire insurances, home theft, marine insurance, etc.). Nonetheless, there is another kind of risks that have an additional detail: the lack of a definite maximum amount. For example, an insurance for major medical expenses. This limit becomes an additional task for actuaries, it can be set since the beginning of the contract’s negotiation, with a limit agreed by the insured, or the risk can be transferred to a reinsurance company.

In order to turn insurances into a lucrative business, insurance companies have large portfolios, that is, a large amount of stored primes. The economic resources of these portfolios cannot be spent by the enterprise, since they must be invested in such a way that they can cover for their future obligations with the insured: the payment of claims. This introduces a whole new fundamental concept for insurance companies and actuaries: the technical reserve.

Calculating the technical reserve

If we knew for certain the exact amount of primes that the insurance company will receive (income) and the payments for claims that this will hand out to it’s insured (expenses), calculating the reserve would come down to a simple difference between the present value of the income and present value of the expenses (let’s remember that by present value we mean the actual value of money being altered by interest rates). This differences will indicate us the amount of money that the insurance company must have in order to fulfill its operation.

Nonetheless, uncertainty of these flows of money requires actuarial calculations in order to constitute the corresponding amount of reserves to the risks that were transferred from the insured to the insurance company.

The described reserve is known as a mathematical reserve, the technical reserve is slightly more robust, since it also considers the payment of the claims that have already occurred but for some reason have not been reported to the insurance company, and those that have been reported but that the exact amount to be paid has not been calculated, that is, that the lost value has not yet been established.

These reserves are, after all, client’s money and thus there exists a regulatory framework that is in charge of controlling all insurance companies, so that an economic stability is assured and user’s public interest is maintained. This regulation is established by the National Commission of Insurance and Finance.


Retaking the idea of claims that do not have limit, insurance companies usually transfer the associated risk of big losses. For that, they strike deals with enterprises that insure the risks taken by the insurance companies: reinsurance companies.

As actuaries in an insurance company, it is important to analyze options to reduce capital requirements, that is why they transfer risks to a reinsurer. Naturally, they also yield part of the primes of all the insured. Insured usually have no knowledge of the reinsurance company that supports the enterprise from which they bought the insurance policy, and it is not necessary, since contracts between insurance and reinsurance companies do not involve clients.

Reinsurance companies play a very important role in the financial sector, since they are responsible for covering catastrophic cases, without them it would be impossible to solve an economic crisis, a natural disaster in a city with high economic activity, a leak on a petroleum platform, etc. All this because insurance companies do not have the financial capacity to cover the expenses of insuring losses of that magnitude.

Social Security

Social Security can be defined as protection given to all the agents in a society, coming from society itself as a whole, but administered by the government. It is executed through programs financed by society, destined to mitigate impact of contingencies such as death, work-related accidents, disease, old age, among others.

An actuary’s work in this area is to calculate the correct amount of contributions, which will be represented with the primes, likewise, they are responsible for the correct investment of funds. Calculations in this area are often inefficient and the bureaucracy that surrounds them does not allow optimization. This is doubtlessly a red flag of social interest in which actuaries must intervene.

Private pensions

One of the most important contingencies that social security must cover is old age, the cost for trying to maintain retired worker’s living standards is very high.

The complexity of establishing government programs to cover for this is huge. In our country, the dynamic goes as follows: social security is in charge of gathering said funds and invests them until a worker’s retirement, so they have the economical possibility of acquiring an annuity on the private sector. An actuary’s stellar job in this sector is to calculate thus mentioned annuities, that function as pensions, when acquired by inactive laborers. As seen previously, the price of these contracts depends a lot on the behavior of a population’s mortality and the amount of the population that will be insured.


Even though insurance is the traditional field for actuary, knowledge within the profession has made it possible for actuaries to gain some terrain in the financial sector. By financial sector we refer mainly to intermediaries such as private and development banks, brokers, investment fund administrators, etc.

Financial Risks

By risk, we refer to the chance of an event causing economical losses. Financial risks are those related with the possible loss generated in financial activities, such as unfavorable movements on interest rates, exchange rates or in the price of stocks.

Financial entities do not seek to eliminate these risks, but to manage and control them, for this, they must identify and quantize them. Financial risk can be categorized in four general groups:

  1. Market Risk: All financial instruments that operate among entities and people are subject to the financial markets component’s volatility, such as exchange rates, interest rates or the value of stocks. This risk aims to measure how instruments (loans, stocks, derivatives, etc.) are held by institutions, affected by changes in the market. For example, it measures how the price of a mortgage in Mexican pesos, sold to a bank operating in euros/dollars, changes.
  2. Credit Risk. It refers to being subject to the unfulfillment of the counterparts with whom agreements have been made, that is, not being paid what you had anticipated. This risk is usually linked to the main activity of the banking sector: handing out credits to individuals or investment and loans between other financial institutions.
  3. Liquidity Risk. Related to having a deficit in the capability of financial institutions for covering its obligations in the short run, that means a lack of cash or other assets of easy transaction, to pay for its debts in the next few days. This can also be seen as the lack of equilibrium between a debt’s deadline and an institution’s estimated income (mismatched balance).
  4. Operational Risks. Although it is not well defined, this risk concerns financial losses caused by failures and insufficiencies of procesess, people, internal systems, technology and the presence of unseen external events.

If these risks are not being constantly monitored, they could turn into huge losses for financial institutions and thus, the public in general. For this reason exists a regulatory organization, the National Securities Commission, which stablishes, among other things, certain limits to risks that may not exceed a company’s portfolio. We will now explain what a portfolio is.

Investment Portfolios

All the money gathered by financial institutions must be invested with the objective of generating income for the clients and the business.

Deciding where and how much to invest from the portfolio is not an easy task, it is impossible to guarantee gains if investment is done on risky assets.

Financial Derivatives

The market contains a great variety of financial products (financial assets) and they represent a value to who acquires them, the most common of these are those whose value depends exclusively on their characteristics.

Financial Derivatives can be defined as those products whose value depends on the price of another asset, This asset is known as an underlying asset and has the peculiarity that it’s value varies with time.

To make this subject clearer, let’s think of a very simple underlying asset: gold. Gold is an asset because it can be bought and it represents a value. Its price today depends exclusively on the amount of gold being traded, and that value may change in the future, since it depends on may factors such as the global economy, supply and demand, global central banking decisions, etc.

A mining company (that sells gold) has a very close relation with a jewelry company (that buy gold). For its administration, both companies strike a deal for a ton of gold next year, they agree that this contract has no value when it is struck, but next year the jewelry will pay the mining company a quantity X in exchange for the ton of gold. This is the simplest of underlying financial assets, known as a futures contract. With this asset both companies stop being subject to the fluctuations in the value of gold for a year’s term, neither the gold buyer or the gold seller needs to worry about rises and falls in the prices, since they have committed to making the transaction for the quantity of X. As an actuary, we must give X a value that makes the contract just for both companies.

Derivatives can be made over any underlying asset with a variable price, and the contract can have different objectives.


This discipline is usually groomed by applied mathematics, but the lack of those
in our country led for actuaries to cover an important part of that area on academical and professional levels.

Statistics is a branch of mathematics that deals with collecting, ordering and analyzing data. It represents a fundamental pillar on the university’s program since, as seen before, data shown by experience allows us to project scenery that helps us make a decision.

Analysis of increasingly larger databases has helped support decision making of different economic and political agents.

There are actuaries applying diverse techniques of statistics in the private sector too, such as pollsters dedicated to making market studies, likewise, industries related with diverse fields of economic activity. In our country’s democratic process, actuaries have participated by designing polls and counts related to elections, through their services lent to various consulting companies or to the mass communications media. Lately, most members of the Technical Assessment Committee of the Federal Elections Institute (IFE) in charge of the quick counting of the votes have been actuaries.

Statistics has various subdisciplines, such as multivaried analysis, linear models, survival analysis, statistical quality control, sampling and analysis of time series, just to mention a few.

Operations Investigation

Perhaps one of the disciplines least related to actuary (on a worldwide level where traditional areas are common) are Operations Investigations, which is usually associated with professions such as engineering. This subject, before 2000, was optional for study plans in the Faculty of Sciences, but many students of the program studied it, and due to the lack of professionals on this field, program’s graduates developed on this area of diverse industries.

One of Operations Investigations main objective is to include the scientific method on processes that need some kind of optimization (that is, finding maximums and minimums of every process).

Some examples of traditional applications of Operations Investigation:

  • Production Problems: If there’s different kinds of machinery, that vary on time and resources to make different kinds of products, how many of each must be produced in order to maximize profits?
  • Distribution problem: If you wish to distribute a certain product and you know the points of sale and needs each has, which would be the optimal route to take in order to cover the demand, minimizing costs?
  • Mix Problem: If a company’s product making varies exclusively on the percentages of raw materials employed and a budget is set, which would be the optimal amount for each product if you are trying to maximize profits?

Such as these, we could keep mentioning a great deal of examples of cases where they are employed.

Computational Systems

Due to the logical-structured form in which mathematics are used by an actuary in order to solve problems, it is possible to enter the world of informatics. One of the most demanded tasks of the field is automation of processes, since it represents a considerable saving of time and human capital. The processes that we are talking about are varied, here are some examples:

  • Updating a database about clients of a mortgage for a bank.
  • Statistical analysis of risks caused by daily changes on interest rates for an investment portfolio.
  • Calculating technical reserves for all the clients of an insurance company.
  • Bartering stocks when its value reaches a given limit.

As actuaries we must not only understand the reach of diverse programming languages when automating processes, but to also find the optimal method to get them done.