由於人口死亡率的改善，全球人口高齡化現象已成為各國重視的議題，此人口結構的重大改變除了增添國家經濟發展的變量，所導致的長壽風險更衝擊著政府退休基金以及提供年金商品的保險公司。本研究將探討唐提年金制度之運作，期望能以唐提年金作為政府以及保險公司解決長壽風險之工具。 引用Piggott et al. (2005)之GSA模型(Group Self-Annuitization)，並以人口資料庫(Human Mortality Database)中之台灣男性死亡率資料進行情境模擬分析。相較于Piggott et al. (2005)，本文為探討未來死亡率改善趨勢對給付之影響，使用Lee-Carter死亡率模型來預估未來死亡率；另外，不同於Piggott et al. (2005)假設固定的投資報酬率，本文考慮每期投資報酬率之波動作為給付計算的重要參數之一。 本研究發現(1).不管是哪種投資組合當中，每期的平均年金給付隨著計劃時間增加。(2).每期的平均年金給付以及給付之分配在股票部位越高的投資組合中有越高的波動性。(3).GSA模型當中， 死亡率變數對於平均年金給付的影響較投資報酬率變數為大。另外，本文亦比較唐提年金制度與確定給付制度之不同：(1).唐提年金俱有充分的基金儲備特色，基金破產機率有限。(2). 在唐提年金體制下，退休金計劃提供者無需承擔基金投資風險。 / Tontine annuity schemes are introduced as a solution for annuity providers and governments to alleviate longevity risk. Applying Taiwan male mortality data to Group Self-Annuitization (GSA) as proposed in Piggott et al. (2005), this paperuses the Lee-Carter model, which incorporates longevity risk, in a simulation study to demonstrate how benefit payments increase in elder ages underdifferent scenarios. Unlike Piggott et al. (2005), we include deviations in both mortality and rate of return from expectations to compare benefit payments amongdifferent portfolios. Moreover, this paperdescribes the two features by whichtontine annuity schemesprevail overTaiwan’s Labor Insurance Annuity Schemes (LIAS): First, tontine annuity schemes are almost always fully funded. Second, the plan sponsor of tontine annuity schemesdoes not need to bear the investment risk.

量子擾動及挫折性兩者均可破壞絕對零溫的磁序，為近代凝態物 理關注的有趣現象。在外加橫場下的三角晶格易辛反鐵磁兼具量子臨 界現象(quantum criticality)及幾何挫折性，可謂量子磁性物質之一典 範理論模型。本論文利用平衡態及非平衡態量子蒙地卡羅(quantum Monte Carlo)方法探測三角晶格易辛反鐵磁之量子相變，其界定零溫 時無磁性的順磁態及具 Z6 對稱破缺的有序態(所謂時鐘態)。這裡的 量子蒙地卡羅方法為運用算符的零溫投射(zero-temperature projector) 及隨機序列展開(stochastic series expansion)演算法。在非平衡模擬 中，我們分別沿降溫過程及量子絕熱過程逼近量子相變點，藉此我們 得到動力學指數，及其它相關臨界指數。 / The destruction of magnetic long-range order at absolute zero temperature arising from quantum fluctuations and frustration is an interesting theme in modern condensed-matter physics. The triangular lattice Ising antiferromag- net in a transverse field provides a playground for the study of the combined effects of quantum criticality and geometrical frustration. In this thesis we use quantum Monte Carlo methods both in equilibrium and non-equilibrium setups to study the properties of the quantum critical point in the triangular lattice antiferromagnet, which separates a disordered paramagnetic state and an ordered clock state exhibiting Z6 symmetry breaking; The methods are based on a zero-temperature projector algorithm and the stochastic series ex- pansion algorithm. For the non-equilibrium setups, we obtain the dynamical exponent and other critical exponents at the quantum critical point approached by slowly decreasing temperature and through quantum annealing.