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| Title: | 隨機矩陣理論應用於財產保險業損失率的三個研究
The Three Studies on Applying Random Matrix Theory to Loss Ratios for General Insurance Companies |
| Authors: | 陳哲斌
Chen, Che-Pin |
| Contributors: | 蔡政憲
Tsai, Chenghsien
陳哲斌
Chen, Che-Pin |
| Keywords: | 隨機矩陣理論
最佳商品組合
風險傳遞網路
逐步最小二乘二次規劃法
冪矩陣
門檻網路
最小生成樹
分群演算法
反向參與率
Wishart 隨機過程
動態系統
橢圓幾何
Random Matrix Theory
optimal product portfolio
risk transmission network
Stepwise Least Squares Quadratic Programming
power matrix
threshold network
Minimum Spanning Tree
clustering algorithm
Inverse Participation Ratio
Wishart stochastic process
dynamic system
ellipsoid geometry |
| Date: | 2025 |
| Issue Date: | 2025-08-04 14:10:00 (UTC+8) |
| Abstract: | 隨機矩陣理論可以用於處理數據相互間的雜訊，本論文為以隨機矩陣理論 (RMT) 研究三個議題：最佳商品組合、風險傳遞網路與時段間動態系統，並以1991-2022年美國財產保險公司的資料進行實證分析。
最佳商品組合為以單一保險公司的商品損失率與核保利潤率為研究對象，本研究以RMT方法論重構商品間損失率與核保利潤率的共變異矩陣，藉以最小化綜合損失率，或核保利潤率變異數為目標，計算最佳商品組合。實證上，採用522家股份保險公司，及203 家相互保險公司的商品組合進行分析，發現無論是以綜合損失率或是核保利潤率的變異數為研究目標，RMT方法論，在最小化目標函數上，具有統計上的顯著性，也同時驗證代理人理論的假說。但在降低核保利潤率變異數的目標上，股份保險公司可能會產生公司治理上的困擾。
風險傳遞網路，為以所選定保險公司的綜合損失率為研究對象，以RMT方法重構保險公司間損失率的相關性，結合網路分析方法論，研究保險公司間的損失率相關性的風險樣貌，並再細分為風險連通性、風險傳遞性與風險貢獻度。實證上，選用449家股份保險公司和216家相互保險公司進行分析，並對於2008年金融風暴前後時期的損失率相關性進行研究。研究發現股份保險公司的連通性高於相互保險公司，而在風險傳遞性上，可區分為不同的傳遞群組，相同群組內將具有穩定的損失傳遞性，此特性可以提供監理機關進行分群監理或再保險公司採用分群風險溢價的參考。另外，研究發現金融風暴時期的網路結構的連通性沒有變化，但風險傳遞網路有局域化的現象，表示保險公司金融風暴期間有進行風險控管甚至於隔離的結果。
時段間動態系統，以所選定保險公司綜合損失率的時段間共變異矩陣為一動態系統，經過RMT方法重構後，研究在不同時段間的相似性或者有極限行為。實證上，選用449家股份保險公司，216家相互保險公司進行分析。研究發現損失率的年度變化率的共變異數間，具有均值回復的特性，符合Wishart 隨機過程的有效性測試。研究中，輔以橢球幾何的方式觀察共變異矩陣的動態行為，發現球體的方向性不具有預測性，也就是特徵向量無法發現極限動態行為，以及主成份主導著損失率變化率在時間上的演化。
This paper employs Random Matrix Theory (RMT), a methodology capable of addressing noise among data, to study three topics: optimal product portfolio, risk transmission networks, and intertemporal dynamic systems. An empirical analysis is conducted using data from U.S. property insurance companies spanning 1991 to 2022.
An optimal product portfolio is defined by minimizing the variances of loss ratios and underwriting profit margins for products from an individual insurance company. In this study, the RMT methodology is employed to reconstruct the covariance matrices of both loss ratios and underwriting profit margins among products, with the goal of computing the optimal product portfolio by minimizing either the overall loss ratio or the variance of underwriting profit margins. Empirical analysis of product portfolios from 522 stock insurance companies and 203 mutual insurance companies reveals that, regardless of whether the objective is to minimize the variance of the overall loss ratio or that of underwriting profit margins, the RMT methodology achieves statistically significant improvements over the empirical portfolio, thereby supporting the agent theory hypothesis. However, when the objective is to minimize the variance of underwriting profit margins, stock insurance companies may encounter corporate governance issues.
The risk transmission network examines the correlation patterns of loss ratios among insurance companies by integrating RMT with network analysis methodologies. The study delves into risk characteristics, including connectivity, transmissibility, and contribution. Empirical data from 449 stock insurance companies and 216 mutual insurance companies' combined ratios are analyzed, with a focus on the periods before and after the 2008 financial crisis. Findings indicate that stock insurance companies exhibit higher connectivity than mutual insurance companies. Furthermore, insurers can be categorized into distinct groups with stable loss ratio transmissibility within each group, providing insights for regulators to implement group-based supervision or for reinsurers to adopt group-based premium strategies. During financial crises, the connectivity of the network structure remains unchanged; however, localized phenomena emerge, suggesting that insurers managed risks or implemented isolation measures during such periods.
The intertemporal dynamic system uses the loss ratio covariance matrix, reconstructed via RMT, as a dynamic system to study similarities or limiting behaviors across time periods. Empirical analysis involving 449 stock insurance companies and 216 mutual insurance companies reveals that the covariance of annual loss ratio changes exhibits a mean-reverting property, validating the effectiveness of the Wishart random process. Supplemented by ellipsoid geometry to observe the dynamic behavior of the covariance matrix, the study finds that the directionality of the ellipsoid lacks predictability, indicating that eigenvectors do not reveal limiting dynamic behavior. Additionally, principal components dominate the temporal evolution of loss ratio changes. |
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| Description: | 博士
國立政治大學
風險管理與保險學系
106358503 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0106358503 |
| Data Type: | thesis |
| Appears in Collections: | [風險管理與保險學系] 學位論文
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