Every insurer lives with an uncomfortable question: how much capital does it need to survive a bad year, the kind that comes once in two hundred? Risk-based solvency regimes, from Solvency II in Europe to the Requerimiento de Capital de Solvencia (RCS, the solvency capital requirement) supervised by the Comisión Nacional de Seguros y Fianzas (CNSF, National Insurance and Surety Commission) in Mexico, answer with a precise definition: capital must cover the worst expected fall in own funds over a one-year horizon at a 99.5 percent confidence level. Formally, the requirement is approximated as the value at risk of the change in own funds.
$$\mathrm{SCR}\;=\;\operatorname{VaR}_{99.5\%}\!\big(\Delta \text{Own funds}_{\,0\to 1}\big)$$The definition is elegant. The calculation, by contrast, can be brutal, and that is where artificial intelligence has begun to change the rules of the game.
The nested calculation problem
Estimating that quantile requires knowing the distribution of own funds one year from now. And valuing the insurance liabilities in each of those future states of the world often requires, in turn, a stochastic valuation: financial options and guarantees, dynamic policyholder behavior and nonproportional reinsurance rarely have closed-form solutions. The result is nested simulation: thousands of outer scenarios describing where the market will be in a year and, within each, thousands of inner paths to value the portfolio. The product of the two, a million valuations or more, turns a conceptually simple calculation into a computing load that can take days.
The industry knows the traditional shortcut: the standard formula, which aggregates risk modules with fixed correlation matrices. It is robust and auditable, but by design it does not capture each company's particular risk profile. The internal model, truer to that profile, runs into the wall of nested calculation. Between the simplicity of the formula and the cost of the full model lies the territory of proxy models.
Learning the own funds function
A proxy model does not simulate: it approximates. The idea is to treat own funds one year ahead as a function of a handful of risk factors (interest rates, credit spreads, equities, mortality, lapses) and to learn that function just once. After that, evaluating the 99.5th percentile takes milliseconds, because all it takes is applying the learned function to a million outer scenarios.
The most widespread technique is Least Squares Monte Carlo (LSMC): you run many outer scenarios with very few inner paths each, sometimes just one, and fit by least squares a function that averages out the noise. In its general form, the target value is approximated by a combination of basis functions:
$$\widehat{f}(\mathbf{x})\;=\;\sum_{k=1}^{K}\beta_k\,\phi_k(\mathbf{x})$$where $\mathbf{x}$ collects the risk factors and the $\phi_k$ are basis functions, traditionally polynomials. The other classic approach, the replicating portfolio, looks for a set of financial instruments whose value mimics that of the liabilities scenario by scenario. Both share the same promise: replacing an expensive valuation with a cheap evaluation.
Where machine learning comes in
Polynomial LSMC works, but it struggles when the relationship between risks and own funds is markedly nonlinear or when factors interact in complex ways. Raising the degree of the polynomial multiplies the terms and reintroduces instability. This is where machine learning offers more expressive families of functions, either for the $\phi_k$ or directly for $\widehat{f}$:
- Gradient boosting on trees, which captures nonlinearities and interactions without the actuary having to specify them in advance.
- Neural networks, able to approximate high-dimensional valuation surfaces with relatively few parameters per factor.
- Gaussian processes, which in addition to an estimate provide a measure of uncertainty, extremely valuable for knowing where the proxy is reliable and where it is not.
The advantage is not only speed. A good proxy makes it possible to recalculate capital in response to market moves almost in real time, run sensitivity analyses, perform analysis of change and build the multiyear projections required by the Own Risk and Solvency Assessment (ORSA). It turns capital from a number produced once a quarter into a living management tool.
Actuarial judgment cannot be approximated
A proxy is, by definition, a model of a model, and it carries two layers of error. The greatest risk lives in the tail: the 99.5th percentile sits precisely where data are scarcest and where a function fitted to the center of the distribution is most likely to fail. That is why validation discipline is non-negotiable. The proxy must be tested against full valuations in out-of-sample test scenarios, its fit in the extreme region must be monitored, and a good overall $R^2$ must not be mistaken for accuracy where it really matters.
The professional bodies have worked on this ground. The Institute and Faculty of Actuaries (IFoA) has published material from its working parties on proxy models and their validation; the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS) contribute research on machine learning applied to valuation and capital. In Mexico, using a full or partial internal model to calculate the RCS is subject to CNSF authorization and review, which places the burden of proof on the company: it must show that its proxy is appropriate, stable and well governed.
The lesson is the usual one, in new clothes. Machine learning does not decide how much capital is enough; it speeds up the calculation so the actuary can spend time on what no function can approximate: choosing the relevant risk factors, judging whether the fit in the tail is credible, understanding the guarantees embedded in the balance sheet and answering, with a signature, to the board and the regulator. The proxy estimates the surface of the risk; judgment decides whether the ground is solid.