arXiv subjects

Mélina Mailhot

Publications and source records attributed to Mélina Mailhot.

5 recordsLinked to original sources

arXiv2026

Morillas-type transformations of copulas and stable tail dependence functions

A stochastic representation and sampling algorithm for Morillas-type copula-to-copula transformations and related distortions of multivariate distribution functions is derived, resulting as a byproduct in a novel sampling scheme for Archimedean and Archimax copulas. This closes a methodological gap and facilitates simulation-based applications of distorted copulas. For stable tail dependence functions (stdfs), a Morillas-type distortion framework is introduced, where monomial distortions with exponents below 1 are shown to preserve stdfs via a domain-restricted Pexider equation analysis. This characterization is leveraged to identify distortions preserving extreme value copulas, and convex combinations of distorted stdfs are proposed to increase flexibility in extremal dependence modeling. The impact of distortions on maximum domain of attraction limits is also analyzed. Explicit limiting EVC distortions are identified under non-restrictive regular variation assumptions. Examples of absolutely monotone distortions allowing to fine-tune the extreme value behavior after distortion, but also of non-regularly varying 2-absolutely monotone distortions are given.

stat.ME↗

arXiv2025

Flexible extreme thresholds through generalised Bayesian model averaging

Insurance products frequently cover significant claims arising from a variety of sources. To model losses from these products accurately, actuarial models must account for high-severity claims. A widely used strategy is to apply a mixture model, fitting one distribution to losses below a given threshold and modeling excess losses using extreme value theory. However, selecting an appropriate threshold remains an open question with no universally agreed-upon solution. Bayesian Model Averaging (BMA) provides a promising alternative by enabling the simultaneous consideration of multiple thresholds. In this paper, we show that an error integration BMA algorithm can effectively detect heterogeneous optimal thresholds that adapt to predictive variables through the combination of mixture models. This method enhances model accuracy by capturing the full loss distribution and lessening sensitivity to threshold choice. We validate the proposed approach using simulation studies and an application to an automobile claims dataset from a Canadian insurer. As a special case, we also study the homogeneous setting, where a single optimal threshold is selected, and compare it to automatic selection algorithms based on goodness-of-fit tests applied to an actuarial dataset.

stat.ME↗

arXiv2025

Probabilistic Crop Yields Forecasts With Spatio-Temporal Conditional Copula Using Extreme Weather Covariates

We introduce a novel forecasting model for crop yields that explicitly accounts for spatio-temporal dependence and the influence of extreme weather and climatic events. Our approach combines Bayesian Structural Time Series for modeling marginal crop yields, ensuring a more robust quantification of uncertainty given the typically short historical records. To capture dynamic dependencies between regions, we develop a time-varying conditional copula model, where the copula parameter evolves over time as a function of its previous lag and extreme weather covariates. Unlike traditional approaches that treat climatic factors as fixed inputs, we incorporate dynamic Generalized Extreme Value models to characterize extreme weather events, enabling a more accurate reflection of their impact on crop yields. Furthermore, to ensure scalability for large-scale applications, we build on the existing Partitioning Around Medoids clustering algorithm and introduce a novel dissimilarity measure that integrates both spatial and copula-based dependence, enabling an effective reduction of the dimensionality in the dependence structure.

stat.ME↗

arXiv2024

Uncertainty Propagation and Dynamic Robust Risk Measures

We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These dynamic uncertainty sets capture the uncertainty surrounding stochastic processes and models, accounting for factors such as distributional ambiguity. Examples of uncertainty sets include those induced by the Wasserstein distance and f-divergences. We further define dynamic robust risk measures as the supremum of all candidates' risks within the uncertainty set. In an axiomatic way, we discuss conditions on the uncertainty sets that lead to well-known properties of dynamic robust risk measures, such as convexity and coherence. Furthermore, we discuss the necessary and sufficient properties of dynamic uncertainty sets that lead to time-consistencies of dynamic robust risk measures. We find that uncertainty sets stemming from f-divergences lead to strong time-consistency while the Wasserstein distance results in a new time-consistent notion of weak recursiveness. Moreover, we show that a dynamic robust risk measure is strong time-consistent or weak recursive if and only if it admits a recursive representation of one-step conditional robust risk measures arising from static uncertainty sets.

q-fin.RM↗

arXiv2020

Modeling and measuring incurred claims risk liabilities for a multi-line property and casualty insurer

We propose a stochastic model allowing property and casualty insurers with multiple business lines to measure their liabilities for incurred claims risk and calculate associated capital requirements. Our model includes many desirable features which enable reproducing empirical properties of loss ratio dynamics. For instance, our model integrates a double generalized linear model relying on accident semester and development lag effects to represent both the mean and dispersion of loss ratio distributions, an autocorrelation structure between loss ratios of the various development lags, and a hierarchical copula model driving the dependence across the various business lines. The model allows for a joint simulation of loss triangles and the quantification of the overall portfolio risk through risk measures. Consequently, a diversification benefit associated to the economic capital requirements can be measured, in accordance with IFRS 17 standards which allow for the recognition of such benefit. The allocation of capital across business lines based on the Euler allocation principle is then illustrated. The implementation of our model is performed by estimating its parameters based on a car insurance data obtained from the General Insurance Statistical Agency (GISA), and by conducting numerical simulations whose results are then presented.

q-fin.RM↗