Paper: arXiv 2302.06668

Authors: Hamed Amini, Zhongyuan Cao, Andreea Minca, Agnès Sulem

Abstract

We study multidimensional Cramér-Lundberg risk processes where agents, located on a large sparse network, receive losses form their neighbors. To reduce the dimensionality of the problem, we introduce classification of agents according to an arbitrary countable set of types. The ruin of any agent triggers losses for all of its neighbours. We consider the case when the loss arrival process induced by the ensemble of ruined agents follows a Poisson process with general intensity function that scales with the network size. When the size of the network goes to infinity, we provide explicit ruin probabilities at the end of the loss propagation process for agents of any type. These limiting probabilities depend, in addition to the agents’ types and the network structure, on the loss distribution and the loss arrival process. For a more complex risk processes on open networks, when in addition to the internal networked risk processes the agents receive losses from external users, we provide bounds on ruin probabilities.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly sophisticated mathematical extension of the multidimensional Cramér-Lundberg risk process to large sparse networks using fluid/large-system limits. However, it is a purely theoretical paper with minimal to no empirical data validation or practical backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Compute Ruin Probabilities in Large Stochastic Risk Networks] --> B[Inputs: Network Structure, Loss Distribution & Scaled Poisson Loss Arrivals]
    B --> C[Methodology: Dimensionality Reduction via Arbitrary Agent Types]
    C --> D[Model Loss Propagation: Ruined Agents Trigger Losses for Neighbors]
    D --> E[Analysis: Take Network Size to Infinity Limit]
    E --> F[Outcome 1: Exact Limiting Ruin Probabilities for Closed Networks]
    E --> G[Outcome 2: Ruin Probability Bounds for Open Networks with External Losses]