一、研究之目的： 保險旨在分散危險─使投保人所遭受之損失轉由保險業者吸收承擔，於事故發生後能 獲得應有之保障。目前國內壽險市場，儲蓄性質之險種所佔比率極高，若保險公司因 經營不善而無法支付俱務時，則投保人多年之積蓄將付諸流水，造成社會問題。 近年來，國人對保險有更深一層的認識，認為它是有效的危險管理方法之一，於是對 保險的需求日增。同時，美國保險公司亦逐登台經營業務。且對國人開放經營保險業 務亦是指日可待。在不久之將來，我國保險市場將趨於紛亂，所以如何監管保險公司 ，以保護投保大眾，乃為重要課題。 目前保險主管機關對各保險公司實施年度檢查，仍偏重於傳統性之監督方法，即檢查 各公司之各種經營是否按照有關法令規定。而各財務比率對保險公司失卻清償能力影 響之幅度未深入分析，且未對這些財務比率作整體評估，計算總指標作為分類的標準 。本篇論文乃針對目前財務檢查若干缺失，藉統計方法建立正常範圍與適當模型，評 估各財務比率對失卻清償能力影響幅度並且計算總標值（失卻清償能力之機率值）， 以供主管機關參考。 二、研究架構 本論文研究程序，可歸成四個步驟： １．公司樣本 本論文是以國內八家壽險公司與BEST REPORT 刊載５２家壽險公司為研究樣本。 ２．財務比率 第二步驟是如何挑選適當財務比率來衡量壽險公司之經營績效。本篇論文以Ａ．Ｍ． BEST公司評價制度，NAIC的保險監理資訊制度，英國邊際清償與我國財政部保險業務 檢查手冊等所採用４８財務比率中篩選適合的財務比率以評估壽險公司失卻清償能力 與否。 ３．研究方法 本篇論文研究方法分成二部份：一是國內八家壽險公司採用離位者測定，另一是美商 ５２家壽險公司採用虛擬應變數迴歸方法。 ４．評估 國內８家壽險公司採用離位者測定方法，釐訂各財務比率的可接受範圍（正當範圍） 。 美商５２家壽險公司採用虛擬應變數迴歸方法作整體評估，計算壽險失卻清償能力的 機率。

In this thesis, we propose many developments in the context of Structural Similarity. We address both node (local) similarity and graph (global) similarity. Concerning node similarity, we focus on improving the diffusive process leading to compute this similarity (e.g. Commute Times) by means of modifying or rewiring the structure of the graph (Graph Densification), although some advances in Laplacian-based ranking are also included in this document. Graph Densification is a particular case of what we call graph rewiring, i.e. a novel field (similar to image processing) where input graphs are rewired to be better conditioned for the subsequent pattern recognition tasks (e.g. clustering). In the thesis, we contribute with an scalable an effective method driven by Dirichlet processes. We propose both a completely unsupervised and a semi-supervised approach for Dirichlet densification. We also contribute with new random walkers (Return Random Walks) that are useful structural filters as well as asymmetry detectors in directed brain networks used to make early predictions of Alzheimer's disease (AD). Graph similarity is addressed by means of designing structural information channels as a means of measuring the Mutual Information between graphs. To this end, we first embed the graphs by means of Commute Times. Commute times embeddings have good properties for Delaunay triangulations (the typical representation for Graph Matching in computer vision). This means that these embeddings can act as encoders in the channel as well as decoders (since they are invertible). Consequently, structural noise can be modelled by the deformation introduced in one of the manifolds to fit the other one. This methodology leads to a very high discriminative similarity measure, since the Mutual Information is measured on the manifolds (vectorial domain) through copulas and bypass entropy estimators. This is consistent with the methodology of decoupling the measurement of graph similarity in two steps: a) linearizing the Quadratic Assignment Problem (QAP) by means of the embedding trick, and b) measuring similarity in vector spaces. The QAP problem is also investigated in this thesis. More precisely, we analyze the behaviour of $m$-best Graph Matching methods. These methods usually start by a couple of best solutions and then expand locally the search space by excluding previous clamped variables. The next variable to clamp is usually selected randomly, but we show that this reduces the performance when structural noise arises (outliers). Alternatively, we propose several heuristics for spanning the search space and evaluate all of them, showing that they are usually better than random selection. These heuristics are particularly interesting because they exploit the structure of the affinity matrix. Efficiency is improved as well. Concerning the application domains explored in this thesis we focus on object recognition (graph similarity), clustering (rewiring), compression/decompression of graphs (links with Extremal Graph Theory), 3D shape simplification (sparsification) and early prediction of AD. / Ministerio de Economía, Industria y Competitividad (Referencia TIN2012-32839 BES-2013-064482)