Actuary Job Interview – Technical Questions

The assumption of normally distributed error terms in linear regression is crucial for several reasons. It allows for valid statistical inference, as hypothesis tests and confidence intervals rely on normality assumptions. Additionally, normality ensures that the model’s predicted values are unbiased and efficient, providing accurate estimates of the dependent variable.

Standard deviation is a statistical measure used to quantify the dispersion or volatility of a set of data points. In risk measurement, it represents the variability of investment returns or insurance losses. A higher standard deviation indicates a greater level of risk, as the potential outcomes are more widely spread around the mean.

Credibility theory is a statistical framework used to estimate risks and predict future outcomes by combining historical data with external information. Actuaries apply credibility theory to enhance the accuracy of loss reserving, premium pricing, and underwriting decisions, particularly in situations where there may be limited or incomplete data.

Parametric statistical models make assumptions about the underlying probability distributions of the data, such as the normal distribution for linear regression. Non-parametric models, on the other hand, do not make explicit distributional assumptions and instead focus on estimating relationships or making predictions based on the data itself.

Survival analysis is a statistical technique used to analyze time-to-event data, such as the time until an insurance claim is filed or a policyholder terminates coverage. Actuaries employ survival analysis to estimate survival probabilities, calculate policy values, and assess the financial impact of events that occur over time.

Correlation measures the strength and direction of the linear relationship between two variables. In actuarial analysis, understanding correlation is essential for modeling dependencies between risks, such as in the construction of multi-line insurance products or the assessment of portfolio diversification benefits.

The time value of money recognizes that a dollar received today is worth more than a dollar received in the future due to the potential for investment earnings. Actuaries use the time value of money principles in various calculations, including discounting future cash flows, determining reserves, and pricing insurance policies.

For long-tail insurance lines, such as liability or workers’ compensation, actuaries need to estimate future claim costs that may not be fully settled for many years. The calculation typically involves analyzing historical claim patterns, assessing the impact of inflation and legal developments, and applying actuarial techniques like loss development triangles and trend analysis.

Credibility weighting is a technique used in loss reserving to assign different weights to historical loss experience and external data based on their relative reliability or credibility. The weights are determined using statistical methods such as the Bühlmann-Straub credibility formula or Bayesian credibility theory.

Stochastic modeling involves incorporating random variables and uncertainty into models to simulate possible future outcomes. In actuarial risk assessment, stochastic modeling is used to understand the range of potential risks and their associated probabilities. It allows actuaries to account for variability and to evaluate the financial impact of different scenarios, providing a more comprehensive understanding of the potential risks an organization may face.

Frequency refers to the number of insurance claims occurring within a given time period. Severity, on the other hand, represents the monetary amount associated with each claim. Both frequency and severity are important components of insurance claims modeling, as they help actuaries estimate the overall claims experience and determine appropriate pricing and reserving strategies.

The central limit theorem assumes that the data being analyzed are independent and identically distributed (IID) and that the sample size is sufficiently large. It states that regardless of the shape of the underlying distribution, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. If the p-value is below a predetermined significance level (e.g., 0.05), it suggests that the observed data provides evidence against the null hypothesis, leading to its rejection in favor of the alternative hypothesis.

Time-series analysis focuses on studying and modeling data that are collected over time. Actuaries use time-series analysis to identify patterns, trends, and seasonality in insurance and financial data. It helps in forecasting future values, detecting unusual behavior, and understanding the potential impact of time-related factors on risk and pricing.

Assessing the adequacy of an insurance company’s risk capital involves analyzing its risk profile, evaluating potential losses under adverse scenarios, and ensuring that the company has sufficient capital to withstand those losses. This assessment often incorporates actuarial modeling techniques, stress testing, and regulatory requirements specific to the insurance industry.

Credibility in credibility theory refers to the proportion of weight given to observed data versus external data in estimating risks. Actuaries assign higher credibility to observed data when it is more reliable, reducing the impact of external data. Credibility impacts risk estimation by allowing for more accurate and tailored predictions based on the available information.

Risk measures like VaR and CTE quantify the potential losses an organization may face under different scenarios. VaR estimates the maximum loss with a certain confidence level, while CTE provides an expectation of the losses beyond a particular threshold. Actuaries use these measures to assess and manage the financial risks associated with insurance products, investments, or other business activities.

A correlation matrix is a square matrix that shows the pairwise correlations between a set of variables, such as different assets in a portfolio. It is used in portfolio diversification to understand the interdependencies between assets and to construct a portfolio with lower overall risk by combining assets that have low or negative correlations.

Parametric statistical models make assumptions about the underlying probability distribution of the data and estimate the parameters of that distribution. Non-parametric models, on the other hand, do not assume a specific distribution and instead focus on estimating relationships or making predictions based on the data itself, using methods such as kernel density estimation or rank-based tests.

In insurance pricing, credibility theory is used to determine the appropriate weight given to historical data versus external data when estimating risks. By combining these sources of information, actuaries can develop more accurate and tailored pricing models that strike a balance between the observed data’s credibility and the additional insights offered by external data.

To assess the sensitivity of an actuarial model, I would conduct a sensitivity analysis by varying the inputs or assumptions within a reasonable range and observing the resulting impact on the model’s outputs. This analysis helps identify the key drivers of the model and understand the potential risks or uncertainties associated with different factors.

In predictive modeling, credibility refers to the weight given to historical data versus other relevant information when developing the model. Actuaries assign higher credibility to data that is more reliable and representative, leading to more accurate predictions. By considering the credibility of different data sources, actuaries can enhance the model’s accuracy and predictive power.

Copulas are mathematical functions used in actuarial modeling to describe the dependence structure between random variables. They allow actuaries to model dependencies between risks more flexibly than traditional correlation measures, enabling a more accurate assessment of joint probabilities and tail dependence in multivariate analyses.

Multistate modeling involves analyzing transitions between different states or statuses over time. In actuarial applications, it is commonly used to model transitions between health states in the life insurance or disability insurance, allowing actuaries to estimate transition probabilities, survival rates, and expected future cash flows associated with policyholders’ changing circumstances.

Analyzing extreme events or tail risks requires specialized techniques such as extreme value theory or tail estimation methods. Actuaries use these methods to understand the probability of rare and extreme events, assess the potential impact of such events on an organization’s financial stability, and develop risk management strategies to mitigate their effects.

Risk margins are additional reserves added to actuarial estimates to account for uncertainty and unforeseen events. They act as buffers to ensure that the estimated liabilities are sufficiently robust to cover potential adverse developments. Risk margins are commonly used in actuarial reserving to provide a level of prudence and to protect policyholders’ interests.

To assess the appropriateness of a statistical model for a given dataset, I would consider several factors. These include evaluating the model’s goodness-of-fit measures, checking for violations of assumptions, conducting residual analysis, and comparing alternative models. Additionally, I would consider domain knowledge and expert judgment to ensure that the model captures the relevant characteristics of the data.

Overfitting occurs when a statistical model is excessively complex and fits the training data too closely, leading to poor performance on new, unseen data. To avoid overfitting, I would employ techniques such as cross-validation, regularization methods (e.g., Lasso or Ridge regression), and feature selection to ensure that the model generalizes well to new data. Regular monitoring of model performance and assessing its stability over time is also essential.

Tail dependence refers to the extent to which extreme events in one variable are associated with extreme events in another variable. In actuarial risk assessment, understanding tail dependence is crucial for modeling extreme events that may lead to simultaneous or correlated losses. It helps actuaries capture the potential contagion or amplification of risks in portfolios or under extreme scenarios.

Parametric bootstrapping is a resampling technique used to estimate the sampling distribution of a statistic by simulating new samples from a fitted parametric model. In actuarial reserving, parametric bootstrapping can be applied to estimate the uncertainty surrounding reserve estimates, especially in situations where traditional reserving techniques may be inadequate due to complex loss development patterns or limited historical data.