A HYBRID QUANTUM–CLASSICAL FRAMEWORK FOR HIGH-DIMENSIONAL INSURANCE PORTFOLIO RISK MODELLING
With Fat-Tail Awareness
Insurance Risk · High-Dimensional Dependence · Fat Tails · Quantum Computing
THE PROBLEM
Large insurance portfolios combine thousands of interacting sources of risk across catastrophe, cyber, pandemic and other exposures.
Two difficulties appear simultaneously.
The first is dimensionality: thousands of risk factors create an enormous dependence structure.
The second is where the information matters most: insurance capital is determined not by typical outcomes, but by rare combinations in the extreme tail of the portfolio-loss distribution.
Standard Monte Carlo becomes increasingly expensive precisely where observations become scarce, while conventional dependence representations become increasingly difficult to estimate and manipulate as dimensionality grows.
The problem is therefore not merely to simulate more scenarios.
It is to find a representation in which the combinations that determine extreme portfolio loss become computationally visible.
THE IDEA
The paper proposes a hybrid quantum-classical architecture in which different parts of the problem are deliberately represented and computed in different ways.
Classical methods retain the tasks for which they are naturally suited: data preparation, dependence estimation and portfolio interpretation.
Quantum-compatible representations are introduced where dimensionality and rare-event estimation create the greatest computational pressure.
The resulting architecture combines classical dependence modelling, quantum-enhanced generative methods for tail augmentation, quantum amplitude estimation for rare-event risk metrics, and classical post-processing for capital allocation.
RESHAPING THE SPACE
The deeper idea is not simply to accelerate Monte Carlo.
A high-dimensional portfolio can be viewed through many coordinate systems. Some preserve the information relevant to ordinary outcomes; others may better expose the dependence structures responsible for extreme losses.
The objective is therefore to reshape the risk space while preserving the relationships that matter in the tail.
Once represented appropriately, computation can be concentrated on the regions of the distribution carrying the information relevant to portfolio-level capital rather than treating all parts of the probability space as equally informative.
This creates a natural division of labor between classical and quantum computation: classical methods structure and interpret the problem; quantum methods are introduced where their representation and sampling properties may ultimately offer an advantage.
QUANTUM AS AN ARCHITECTURAL CHOICE
The paper is explicitly hybrid.
It does not assume that the complete insurance model should move onto a quantum computer.
Instead, it identifies specific computational modules that can evolve independently as quantum hardware matures, while the overall risk architecture remains usable classically.
The full framework is organized around data preparation, tail-aware distribution generation, rare-event estimation and portfolio-level interpretation, with explicit attention to the hardware and implementation requirements of each stage.
WHY IT MATTERS
Insurance is fundamentally a problem of combinations.
A single risk may be understandable in isolation. Portfolio danger emerges when many risks interact—and particularly when unusual dependencies become important simultaneously.
At sufficient dimensionality, simply adding more data or more simulations does not necessarily make those structures easier to see.
The broader proposition of the research is that complexity can sometimes be made computationally tractable by changing the representation through which it is observed.
The objective is not to simplify away the complexity, but to reshape it into a form in which the patterns that determine extreme outcomes can be found.
RESEARCH STATUS
Independent research · July 2026
Working research paper