The Reinsurance Actuary: contracts, retention, RGRE and cat bonds

Overview of the specialty

No insurer can absorb on its own all the risks it writes. The LISF (Insurance and Surety Institutions Law) makes this an obligation: institutions must diversify and spread their risks through reinsurance or surety reinsurance contracts with other institutions or with foreign reinsurers, or through coinsurance (article 256). The board of directors sets maximum retention limits and a reinsurance committee oversees compliance with the policy.

Reinsurance serves four purposes: it stabilizes results by cutting volatility, protects against catastrophes and accumulations, provides capacity to write risks larger than the company's own capital, and releases solvency capital requirement. In exchange, the cedent pays a premium and takes on a new risk: that the reinsurer will not pay when it is needed.

The Mexican market operates with domestic reinsurers authorized by the CNSF (National Insurance and Surety Commission), representative offices of foreign reinsurers authorized by the CNSF (article 108) and reinsurance intermediaries. Most catastrophe capacity comes from abroad, and only foreign entities registered in the Registro General de Reaseguradoras Extranjeras (RGRE, General Registry of Foreign Reinsurers) kept by the CNSF may accept risks from Mexican institutions (article 107).

The public sector also transfers risk. Since 2006 the Federal Government has sponsored, with the World Bank, some 20 catastrophe bond issues covering earthquake and hurricane. After the September 7, 2017 earthquake in Oaxaca and Chiapas, the bond in force paid 100% of its earthquake coverage, US$150 million; in 2024 US$595 million was placed in four classes running until April 2028, and in 2026 the government complemented that protection with parametric insurance of about US$575 million placed through Agroasemex.

Key functions

Reinsurance program design

Proposes the mix of contracts by line: quota share for new portfolios or those with limited capital, surplus for risks with heterogeneous sums insured, per risk excess of loss for large individual losses and catastrophe excess of loss per event. Quantifies the effect of each alternative on earnings, volatility and the RCS (solvency capital requirement).

Optimal retention

Determines how much to keep per risk and per event using criteria of risk appetite, probability of ruin, cost of capital and market price. Provides the technical basis for the retention limits approved by the board.

Layer pricing

On the reinsurer or broker side, estimates the expected cost of each layer from historical experience brought to current conditions (burning cost), exposure curves and catastrophe models, and adds loadings for volatility, expenses and capital.

Extreme event modeling

Builds per event and annual loss distributions with catastrophe models and extreme value theory, and derives exceedance curves to decide the program's upper limit, for example a 200 or 250 year return period.

Counterparty management

Assesses reinsurers' ratings, concentration and solvency, verifies their RGRE registration and measures how a potential default would affect reinsurance recoverables and the RCS.

Technical accounting and recoveries

Calculates reinsurance recoverables separately from gross reserves, as well as reinstatement premiums, commissions and profit commissions, and reconciles accounts with reinsurers and intermediaries.

Techniques, models and formulas

Reinsurance is applied risk theory: every contract is a function that transforms the cedent's loss distribution. The actuary must know which part of the distribution each structure protects and at what price, and connect that analysis with ruin theory and with the regulatory solvency metric.

Quota share and surplus

Under a quota share, a fixed percentage of every risk, premium and loss is ceded; it reduces exposure proportionally but does not change the shape of the distribution. Under a surplus treaty, the portion of the sum insured above a retention line is ceded, which makes the retained portfolio more homogeneous.

Per risk and catastrophe excess of loss

The reinsurer pays the portion of each loss, or each event, that exceeds a retention, up to a limit. It is organized in successive layers and usually includes reinstatements for an additional premium. It is the tool that cuts off the tail.

Stop-loss

Protects aggregate annual losses when they exceed a percentage of premium, for example from 80% to 120%. It is used in agricultural insurance, group medical expense and small, highly volatile portfolios.

Burning cost and exposure curves

Burning cost takes the historical recoveries the layer would have had, adjusted for inflation and growth, and divides them by the subject premium. When history is scarce, exposure curves are used (for example, the MBBEFD family), which allocate premium according to the share of the sum insured covered by the layer.

Financial reinsurance

Combines risk transfer with a financing component. The CUSF (Single Insurance and Surety Circular) defines it by the fact that the payment commitment to the reinsurer remains even if the cedent ceases operations; it requires prior CNSF authorization case by case and may only be entered into with reinsurers authorized to operate exclusively as such or with foreign reinsurers rated at least AA- (or equivalent).

ILS and catastrophe bonds

A special purpose vehicle issues notes to investors and deposits the principal as collateral; if the event occurs, the principal is paid to the sponsor. Triggers can be parametric, such as the earthquake cat-in-a-grid and the hurricane central pressure cat-in-a-gate used by Mexico's bonds.

Recovery under an excess of loss layer

\[R(X) = \min\{\max(X - d,\,0),\; l\}, \qquad X_{ret} = X - R(X)\]

X is the gross loss, d the retention and l the layer limit (written l xs d). The cedent retains the retention and any amount above d + l not covered by another layer.

Lundberg's inequality

\[\psi(u) \le e^{-R u}\]

ψ(u) is the probability of ruin with initial capital u and R is the adjustment coefficient, which depends on the premium and on the distribution of retained losses. Reinsuring the tail increases R and lowers the ruin bound, even though it costs premium.

Burning cost pricing and rate on line

\[P_{XL} = \frac{\frac{1}{n}\sum_{t=1}^{n} R_t}{1-\lambda}, \qquad ROL = \frac{P_{XL}}{l}\]

R_t are the layer's historical recoveries brought to current conditions, n the number of years and λ the share of premium that covers the reinsurer's expenses, capital and profit. Rate on line expresses the premium as a percentage of the limit.

Regulatory framework in Mexico

LISF art. 256 · CUSF Title 9

Requires risks to be diversified and spread through reinsurance, surety reinsurance or coinsurance. The board sets maximum retention limits on a technical basis (Chapter 9.1), the reinsurance committee oversees compliance (Chapter 3.10) and financial reinsurance requires prior CNSF authorization (Chapter 9.5).

LISF art. 107 · CUSF Title 34 · RGRE

Risk may only be ceded to foreign entities registered in the RGRE, which the CNSF grants at its discretion to first-class reinsurers. The minimum financial strength rating is BBB- from S&P or Fitch, Baa3 from Moody's or the equivalent from A.M. Best and HR Ratings; registration expires on December 31 and is renewed every year. Reinsurers that operate mainly or exclusively with institutions to which they are related are not registered.

LISF arts. 229 and 230 · CUSF Chapter 8.20

Technical reserves are calculated gross, and reinsurance recoverables are estimated separately, only for contracts with genuine risk transfer and adjusted for the probability of counterparty default.

CUSF Title 6 · RCS and counterparty

The RCS is obtained as the sum of the requirements for technical and financial risks, for PML, for other counterparty risks and for operational risk. Reinsurer default enters the simulation of recoverables and the deduction in the PML requirement, which takes into account the counterparty and concentration of ceded reinsurance.

LISF art. 108 · CUSF Title 35

Govern the representative offices of foreign reinsurers and reinsurance intermediaries, which require CNSF authorization and errors and omissions liability insurance.

Case study: per risk excess of loss layer in fire

An insurer with gross net premium income (GNPI) of $400 million in fire buys a per risk excess of loss layer of 5 million in excess of 2 million (5 xs 2), with one reinstatement at 100%. The recoveries the layer would have had over the last 5 years, brought to current conditions, were 0, 2.1, 0, 5.0 and 0.9 million. The reinsurer allocates 30% of the premium to expenses, capital and profit. Figures in millions of pesos.

Effect per loss: a loss of 1.5 does not reach the layer (1.5 retained); a loss of 3.0 recovers 3.0 - 2.0 = 1.0 (2.0 retained); a loss of 8.0 recovers the full 5.0 limit and the cedent retains 3.0: the 2.0 retention plus 1.0 above the layer's 7.0 exhaustion point.
Burning cost: (0 + 2.1 + 0 + 5.0 + 0.9) / 5 = 8.0 / 5 = 1.60 million per year.
Layer premium: 1.60 / (1 - 0.30) = 2.29 million, equivalent to 2.29 / 400 = 0.571% of GNPI.
Rate on line: 2.29 / 5 = 45.7%. Implied payback period: 5 / 2.29 = 2.19 years; this is a working layer expected to be hit frequently.
Reinstatement: if a loss exhausts the 5 million limit, the cedent pays an additional 2.29 × 5 / 5 = 2.29 million to restore the layer for the rest of the policy period.
Compare with a 40% quota share: for the 8.0 loss the cedent would retain 4.8 instead of 3.0, but would cede 40% of all premium (160 million). A quota share shares the business; excess of loss cuts severity.

Lesson: Each structure targets a different part of the distribution. The 8.0 loss also shows that a poorly sized layer hands risk back to the cedent: the program's upper limit should be set with the PML and risk tolerance, not by habit.

Where they work and how they grow

Analyst (0 to 3 years)

Prepares underwriting information for placements (portfolio profiles, loss history, accumulations), runs burning cost and exposure models, and reconciles technical accounts.

Actuary (3 to 7 years)

Prices layers and contracts, builds per event loss models, compares quotes and prepares the analysis of alternatives for the reinsurance committee.

Senior actuary or technical underwriter (7 to 12 years)

Negotiates structures with reinsurers and brokers, sets retentions with the risk function, signs off on capital analyses and leads the renewal of entire programs.

Head of reinsurance or chief actuary (12 years or more)

Answers to the board for risk transfer strategy, counterparty diversification and the use of alternatives such as financial reinsurance or ILS.

Typical employers in Mexico

Mexican reinsurers authorized by the CNSF
Representative offices of global reinsurers in Mexico
Reinsurance intermediaries and international brokers
Reinsurance departments of life, property and casualty, and agricultural insurers
Catastrophe modeling firms
Comisión Nacional de Seguros y Fianzas (CNSF)
Agroasemex and public risk transfer entities
ILS fund managers and investment banks with insurance risk desks

Common job titles

Reinsurance pricing actuaryTreaty technical underwriterCatastrophe modeling analystLife reinsurance actuaryStructuring actuary at a reinsurance intermediaryCounterparty risk analystCeded reinsurance managerHead of reinsurance

Skills and tools

Technical

Risk theory and the collective modelTail distributions and extreme value theoryExperience and exposure ratingCatastrophe modeling and exceedance curvesRuin theory and optimal retentionEconomic capital and RCS methodologyReinsurance technical accounting

Tools

Python and R for simulation and pricingAdvanced Excel for quotes and technical accountsCommercial catastrophe modeling platformsCNSF R and RH-Mex systemsSQL for portfolio and loss profilesDynamic financial analysis tools

Personal

Negotiating with reinsurers and brokersFluent technical and business EnglishDistilling complex risks for the boardCommercial and risk judgment at the same timeWorking under pressure during renewal season

Certification and education

CONAC certification in the relevant line

An actuary who signs technical notes or valuations that incorporate reinsurance needs certification in the relevant line (life, property and casualty, accident and health, or surety).

CAS ACAS and FCAS

Their exams cover reinsurance, layer pricing and catastrophe modeling. They are the benchmark in property and casualty reinsurance.

SOA ASA and FSA

Relevant for life and health reinsurance, where risk premium treaties, coinsurance and financing structures are studied.

CERA

The enterprise risk management credential connects reinsurance design with economic capital and risk appetite. See certification.

Trends reshaping the field

Hardening and market cycles

After years of catastrophe losses and higher cost of capital, reinsurers raised retentions and prices. The cedent's actuary must use models to justify how much to retain and which layers are worth their cost.

Parametric solutions for the public sector

Mexico combines catastrophe bonds with the World Bank and parametric insurance. The technical challenge is reducing basis risk: the index should trigger when the damage is real and not trigger when it is not.

Alternative capital and ILS

Pension funds and institutional investors provide capacity through catastrophe bonds, collateralized reinsurance and sidecars. The actuary translates loss models into investment metrics such as expected loss and probability of exhaustion.

Climate change in the models

Rapid intensification events such as Hurricane Otis force a review of hazard catalogs and vulnerability assumptions. Climate scenario analysis is increasingly part of catastrophe program renewals.

Frequently asked questions

Why can't a Mexican insurer reinsure with just any foreign company?

Because article 107 of the LISF requires the foreign reinsurer to be registered in the RGRE. The CNSF registers only first-class entities with a minimum financial strength rating and sufficient information on their solvency, and registration is renewed every year.

What is the difference between proportional and non-proportional reinsurance?

In proportional reinsurance, the cedent and the reinsurer share premiums and losses in the same proportion, and the reinsurer pays a commission. In non-proportional reinsurance, the reinsurer pays only the portion of the loss that exceeds a retention, in exchange for a premium calculated on the risk of the layer.

What is a catastrophe bond and how has Mexico used it?

It is an instrument in which investors contribute capital they lose if a defined event occurs; in return they receive a coupon. Mexico has been a repeat sponsor with the World Bank since 2006: it received US$150 million after the September 2017 earthquake and in 2024 placed US$595 million against earthquake and hurricane.

Does reinsurance reduce required capital?

Yes, when it genuinely transfers risk: it reduces the retained loss in the extreme scenarios measured by the RCS. But the reduction is adjusted for the risk that the reinsurer will not pay, so the quality and diversification of counterparties matter as much as the structure.