arXiv subjects

Andrew Fleck

Publications and source records attributed to Andrew Fleck.

3 recordsLinked to original sources

arXiv2026

Geometry Induced Contraction Degradation and Stabilization of Learning Enabled Observers

Learned perception models are increasingly used as measurement maps within nonlinear observers, mapping high dimensional sensory inputs to low dimensional quantities for state estimation. Unlike analytic measurement functions, learned models introduce state dependent Jacobians whose effect on observer stability is rarely characterized. We show that learned measurement geometry enters the observer error dynamics explicitly and rescales Euclidean contraction margins. Under fixed gains, increased measurement sensitivity reduces the certifiable contraction region and can eliminate exponential convergence guarantees. To address this effect, we introduce a representation aware gain normalization that compensates for geometry induced amplification using only local Jacobian information. The proposed approach treats the learned measurement model as a black box and requires no retraining or architectural modification. The normalization removes the dominant sensitivity dependence and restores a uniform Euclidean contraction bound while preserving a simple observer structure. Numerical and real data experiments validate the predicted sensitivity convergence relationship and demonstrate improved robustness and stability in learning enabled observer architectures.

eess.SY↗

arXiv2024

Risk Aggregation and Allocation in the Presence of Systematic Risk via Stable Laws

In order to properly manage risk, practitioners must understand the aggregate risks they are exposed to. Additionally, to properly price policies and calculate bonuses the relative riskiness of individual business units must be well understood. Certainly, Insurers and Financiers are interested in the properties of the sums of the risks they are exposed to and the dependence of risks therein. Realistic risk models however must account for a variety of phenomena: ill-defined moments, lack of elliptical dependence structures, excess kurtosis and highly heterogeneous marginals. Equally important is the concern over industry-wide systematic risks that can affect multiple business lines at once. Many techniques of varying sophistication have been developed with all or some of these problems in mind. We propose a modification to the classical individual risk model that allows us to model company-wide losses via the class of Multivariate Stable Distributions. Stable Distributions incorporate many of the unpleasant features required for a realistic risk model while maintaining tractable aggregation and dependence results. We additionally compute the Tail Conditional Expectation of aggregate risks within the model and the corresponding allocations.

q-fin.RM↗

arXiv2024

Stochastic Loss Reserving: Dependence and Estimation

Nowadays insurers have to account for potentially complex dependence between risks. In the field of loss reserving, there are many parametric and non-parametric models attempting to capture dependence between business lines. One common approach has been to use additive background risk models (ABRMs) which provide rich and interpretable dependence structures via a common shock model. Unfortunately, ABRMs are often restrictive. Models that capture necessary features may have impractical to estimate parameters. For example models without a closed-form likelihood function for lack of a probability density function (e.g. some Tweedie, Stable Distributions, etc). We apply a modification of the continuous generalised method of moments (CGMM) of [Carrasco and Florens, 2000] which delivers comparable estimators to the MLE to loss reserving. We examine models such as the one proposed by [Avanzi et al., 2016] and a related but novel one derived from the stable family of distributions. Our CGMM method of estimation provides conventional non-Bayesian estimates in the case where MLEs are impractical.

stat.ME↗