TITLE:
Entropy as an Indicator for Risk Sharing Pool Quality
AUTHORS:
Miwaka Yamashita
KEYWORDS:
Entropy, Adjacency Matrix, Peer to Peer, Pooling, Risk Sharing
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.15 No.1,
January
21,
2025
ABSTRACT: This study investigates several pooling risk sharing schemes and the measurement of their pool quality as peer to peer (P2P) insurance platforms. The P2P insurance is an emerging and growing insurance scheme that helps each other compensate the pool’s total losses by funding and risk sharing ex-post with a certain rule among the pool participants. The new scheme comes from preliminary empirical research regarding existing P2P insurance. In the end, the schemes are characterized by the rule and the adjacency matrix of the pool, which leverages network theory, and the new risk sharing rule looks like adjusted version of the typical network adjacency matrix, which identifies indicators of pool quality of a new scheme. While assessing effectiveness among several risk sharing rules, it finds that, especially for the new risk sharing scheme, those matrix entropy serves as an indicator of pool quality like volatility and network centrality. Examples illustrate the effectiveness of the proposed model in assessing pool quality. This study contributes to the literature by proposing a new risk sharing scheme, which is based on preliminary empirical research, considering pool quality, and introducing the adjusted version of adjacency matrix as a rule and a tool to model relative relationships among pool participants. It expands the understanding of risk sharing mechanisms in P2P insurance platforms and provides valuable insights for pool management and quality assessment. The study highlights the importance of considering relative relationships among pool participants.