Este trabalho propõe um modelo para a simulação do passivo atuarial de um fundo de pensão brasileiro. As principais fontes de incertezas que influenciam a avaliação do passivo atuarial foram especificadas como variáveis aleatórias e parâmetros do modelo. Diversos cenários são gerados utilizando a técnica de simulação de Monte Carlo e a microssimulação no intuito de determinar o status de cada participante do fundo de pensão modelo para períodos futuros em diferentes nós de uma árvore de cenários. A situação de vida de cada participante, simulada individualmente a cada nó, está condicionada ao seu estado no nó imediatamente antecessor. O resultado é um modelo flexível, que permite a configuração de parâmetros a níveis individuais e possibilita trabalhar com diversas tábuas biométricas, mostrando-se capaz de gerar cenários consistentes, realistas e variados, capturando a essência da incerteza inerente às entidades de previdência complementar e produzindo não só valores únicos e determinísticos de reservas matemáticas e fluxos de caixa atuariais, mas intervalos de valores possíveis com distribuições conhecidas, importantes para a gestão eficiente de um fundo de pensão. A metodologia proposta serve como alternativa ao cálculo atuarial tradicional, que utiliza diretamente as probabilidades das tábuas biométricas, fixas por idade e sexo, para a mensuração dos fluxos de caixa previdenciários e reservas matemáticas. Os dados gerados a partir das simulações servem como dados de entrada para um modelo estocástico completo de Asset-Liability Management (ALM). / This study proposes a model to simulate actuarial liabilities from a pension fund in Brazil. The main uncertainties that affect the liabilities have been specified as random variables and parameters of the developed model. Many scenarios are generated using Monte Carlo simulation and micro-simulation techniques in order to determine the status of each member of the pension fund for future periods in different nodes of a scenario tree. The future of each participant, simulated individually at each node, is conditioned to its status in the immediately predecessor node. The result is a flexible model which allows the parameters configuration at individual levels and that can work with several actuarial tables, showing to be itself able to generate consistent, realistic and sorted scenarios, capturing the uncertainty inherent in pension funds environment and producing not only single and deterministic values for actuarial liabilities and cash flows, but ranges of possible values with known distributions, becoming an important tool for the efficient management of the pension fund. The methodology applied is an alternative to the classic actuarial techniques, that use directly the probabilities from actuarial tables, fixed by age and gender, to calculate the liabilities and the cash flow of the pension fund. The data generated by this model were thought to be inputs for a full multistage stochastic Asset-Liability Management (ALM) model.

Este trabalho propõe um modelo para a simulação do passivo atuarial de um fundo de pensão brasileiro. As principais fontes de incertezas que influenciam a avaliação do passivo atuarial foram especificadas como variáveis aleatórias e parâmetros do modelo. Diversos cenários são gerados utilizando a técnica de simulação de Monte Carlo e a microssimulação no intuito de determinar o status de cada participante do fundo de pensão modelo para períodos futuros em diferentes nós de uma árvore de cenários. A situação de vida de cada participante, simulada individualmente a cada nó, está condicionada ao seu estado no nó imediatamente antecessor. O resultado é um modelo flexível, que permite a configuração de parâmetros a níveis individuais e possibilita trabalhar com diversas tábuas biométricas, mostrando-se capaz de gerar cenários consistentes, realistas e variados, capturando a essência da incerteza inerente às entidades de previdência complementar e produzindo não só valores únicos e determinísticos de reservas matemáticas e fluxos de caixa atuariais, mas intervalos de valores possíveis com distribuições conhecidas, importantes para a gestão eficiente de um fundo de pensão. A metodologia proposta serve como alternativa ao cálculo atuarial tradicional, que utiliza diretamente as probabilidades das tábuas biométricas, fixas por idade e sexo, para a mensuração dos fluxos de caixa previdenciários e reservas matemáticas. Os dados gerados a partir das simulações servem como dados de entrada para um modelo estocástico completo de Asset-Liability Management (ALM). / This study proposes a model to simulate actuarial liabilities from a pension fund in Brazil. The main uncertainties that affect the liabilities have been specified as random variables and parameters of the developed model. Many scenarios are generated using Monte Carlo simulation and micro-simulation techniques in order to determine the status of each member of the pension fund for future periods in different nodes of a scenario tree. The future of each participant, simulated individually at each node, is conditioned to its status in the immediately predecessor node. The result is a flexible model which allows the parameters configuration at individual levels and that can work with several actuarial tables, showing to be itself able to generate consistent, realistic and sorted scenarios, capturing the uncertainty inherent in pension funds environment and producing not only single and deterministic values for actuarial liabilities and cash flows, but ranges of possible values with known distributions, becoming an important tool for the efficient management of the pension fund. The methodology applied is an alternative to the classic actuarial techniques, that use directly the probabilities from actuarial tables, fixed by age and gender, to calculate the liabilities and the cash flow of the pension fund. The data generated by this model were thought to be inputs for a full multistage stochastic Asset-Liability Management (ALM) model.

Este trabalho propõe um modelo para a simulação do passivo atuarial de um fundo de pensão brasileiro. As principais fontes de incertezas que influenciam a avaliação do passivo atuarial foram especificadas como variáveis aleatórias e parâmetros do modelo. Diversos cenários são gerados utilizando a técnica de simulação de Monte Carlo e a microssimulação no intuito de determinar o status de cada participante do fundo de pensão modelo para períodos futuros em diferentes nós de uma árvore de cenários. A situação de vida de cada participante, simulada individualmente a cada nó, está condicionada ao seu estado no nó imediatamente antecessor. O resultado é um modelo flexível, que permite a configuração de parâmetros a níveis individuais e possibilita trabalhar com diversas tábuas biométricas, mostrando-se capaz de gerar cenários consistentes, realistas e variados, capturando a essência da incerteza inerente às entidades de previdência complementar e produzindo não só valores únicos e determinísticos de reservas matemáticas e fluxos de caixa atuariais, mas intervalos de valores possíveis com distribuições conhecidas, importantes para a gestão eficiente de um fundo de pensão. A metodologia proposta serve como alternativa ao cálculo atuarial tradicional, que utiliza diretamente as probabilidades das tábuas biométricas, fixas por idade e sexo, para a mensuração dos fluxos de caixa previdenciários e reservas matemáticas. Os dados gerados a partir das simulações servem como dados de entrada para um modelo estocástico completo de Asset-Liability Management (ALM). / This study proposes a model to simulate actuarial liabilities from a pension fund in Brazil. The main uncertainties that affect the liabilities have been specified as random variables and parameters of the developed model. Many scenarios are generated using Monte Carlo simulation and micro-simulation techniques in order to determine the status of each member of the pension fund for future periods in different nodes of a scenario tree. The future of each participant, simulated individually at each node, is conditioned to its status in the immediately predecessor node. The result is a flexible model which allows the parameters configuration at individual levels and that can work with several actuarial tables, showing to be itself able to generate consistent, realistic and sorted scenarios, capturing the uncertainty inherent in pension funds environment and producing not only single and deterministic values for actuarial liabilities and cash flows, but ranges of possible values with known distributions, becoming an important tool for the efficient management of the pension fund. The methodology applied is an alternative to the classic actuarial techniques, that use directly the probabilities from actuarial tables, fixed by age and gender, to calculate the liabilities and the cash flow of the pension fund. The data generated by this model were thought to be inputs for a full multistage stochastic Asset-Liability Management (ALM) model.

yes / This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme’s projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.

本研究運用的投資組合理論(Portfolio Theory)與免疫理論(Immunization Theory)建構資產負債管理模型，希望在於免除利率風險下，能夠極大化勞保基金的投資報酬率。本研究探討勞保老年給付年金制實行後，勞保基金在資產負債管理之下最適資產配置。我們以勞保局編印之「勞工保險統計年報」中勞保基金民國81年到91年實際投資的資料及勞保局委託研究之精算報告對於老年給付年金制實行後未來勞保基金的給付預測值，在不同年金選擇率以及不同的費率與控管年限下，根據勞保基金資產與負債的存續期間，建議勞保基金最適的投資組合，並計算資產負債管理成本，研究結果發現： 1 年金選擇率為100％及80%時，勞保費率提高至8.3%僅能確保未來30年與40年勞保基金不會因為利率變動而導致基金破產甚至無力清償，但考慮年限為50年時，國內市場無法找到存續期間可以配合的投資工具，無法規避利率風險。年金選擇率為50%時，由於未來各年之勞保的給付獲得舒緩，使得資產配置所需的存續期間也降低，故當勞保費率提高 至8%即可確保勞保基金未來50年可以規避利率風險的危機，且在國內市場上可以找到投資工具配合。 2. 要使勞保基金免於利率風險的考慮年限越長，其投資組合的重心應該從現行的銀行存款移轉到債券及股票與受益憑證。 3. 進行資產負債管理是需要成本的，若以資產負債管理前後效率前緣下的投資報酬率的差異為資產負債管理成本，在年金選擇率100%時資產負債管理平均成本為0.3695%；選擇率80%時平均成本為0.434%；年金選擇率為50%時資產負債管理平均成本為0.384%，研究結果顯示資產負債管理平均成本都低於0.5%以下，故建議勞保基金應盡早進行資產負債管理以因應老年給付年金化後利率風險對於勞保基金財務上的衝擊。 / This paper investigates the Asset-Liability Management for Labor Insurance Fund. We utilize Immunization Theory and Portfolio Theory selection model to immunize the surplus of Labor Insurance Funds against interest-rate fluctuations and to maximize expected return of Labor Insurance Funds simultaneously. In addition, we use the data from Labor Insurance Funds from 1992 to 2002 to demonstrate the implementation of our model. We calculate the optimal asset allocation and the ALM cost under different lump-sum/annuity selection ratio、time horizon and contribution rates. The empirical results from this study show that： 1. Assuming 100% and 80% participants choice annuity, to prevent the insolvency of Labor Insurance Fund from interest-rate fluctuations in 30 and 40 years, the Labor Insurance premium must increase to 8.3%. Assuming 50% participants choice annuity, to prevent the insolvency of Labor Insurance Fund from interest-rate fluctuations in 50 years, the Labor Insurance premium must increase to 8%. 2. To prolong the period over which the Labor Insurance Funds can immunize its surplus against interest-rate fluctuations, a large proportion of the investment asset should be allocate from bank deposit to bond and stock. 3. ALM needs cost. Assuming 100% participants choice annuity, the average ALM cost is 0.3695%.Assuming 80% participants choice annuity, the average ALM cost is 0.434%.Assuming 50% participants choice annuity, the average ALM cost is 0.384%. We find the average ALM cost is very small under any lump-sum/annuity selection ratio. Therefore, we suggest Bureau of Labor Insurance should start to implement ALM as soon as possible to avoid the affect of interest-rate fluctuations.

The key objective of insurance company on money management is asset liability management, as policy asset is solely for paying policy liability. It is true whether it is in case of life insurance, general insurance, or reinsurance. The difficulty of achieving such objective is that the exact cash flow and the exact duration of policy liability are unknown ex ante that requires the asset manager's a good quantitative, financial skill. What is worse is that the variations of cash flow and duration can be huge that is demanding on the asset manager's quantitative, financial skill. Quantitative problem is difficult but qualitative problem can be even more difficult. The specialist problem in insurance industry, which is also known as agency problem in information economics, is notorious. It is because a specialist may no longer work for the insurance company when the long term liability is due and the existing liability portfolio is always composed of myriad policies liability. / The purpose of this thesis is to try to provide solutions to three critical problems in insurance industry. (1) China is the most booming country for insurance at the moment. So, it is selected for discussing about the most difficult problem in modern finance---specialist problem. A structural approach is devised in this thesis to solve such problem. The solution can be generalized to all countries. (2) As many people argue about that modern finance is inapplicable to emerging market, such as China, especially when there are capital account and currency controls, the bond market of China is selected to provide evidence that modern finance is applicable to emerging market even both the capital account and the currency of the country are controlled by the government. (3) The last part of this thesis provides a breakthrough solution to price insurer default option, an embedded option, in insurance company using observable credit default swap price, as the traditional approach needs statistical assumption that is subjective. / Li, Wing Ping Desmond. / Adviser: Frank Youhua Chen. / Source: Dissertation Abstracts International, Volume: 70-06, Section: A, page: 2169. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 64-65). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

不同評估績效的長短顯著地影響基金的經營策略，相較於強調穩健經營的退休基金而言，此因素是否亦影響退休基金的運作，本研究嘗試應用隨機控制理論，將投資績效的時間因素納入決策考量，以隨機微分方程式描述退休基金資產和應計負債的動態隨機行為，以多期基金規劃的觀點，探討時間因素與最適策略之關連性。本研究應用Brennan、Schwartz與Lagnado（1997）的結果至負債導向的退休基金管理，建構多期資產負債管理模型，退休基金持有資產將分類為風險性的股票投資組合、長期債券和短期票券，並考量投資標的短期利率與長期利率之隨機性質，將基金提撥與資產配置視為可調節因子，給定風險評估測度，於不設定投資限制下計算各期最適投資比例及基金提撥；本研究並以私人退休金個案進行模擬分析，結果顯示此基金未來10年之最適提撥率介於4.2﹪與5.1﹪，就不同評估期限而言，5年評估期之提撥率於初期高於10年評估期，基金比率η=0.75之提撥率低於η=1；5年評估期之基金交易行為較10年期明顯劇烈，基金比率較低時，其交易變化程度較小，不同評估年限與基金比率將同時影響退休基金之最適提撥與投資策略。 / Distinct time horizons in measuring investment perfomance significantly influence the financial planning for the money managers. In this study, we explore this issue concerning the pension fund management that has focused on the asset and liability management to meet its future obligations. A stochastic control model is formulated in a continuous-time framework to obtain the closed form solution for optimal strategy. The time variation in expected returns introduced in Brennan, Schwartz and Lagnado（1997）is adopted in obtaining the optimal strategy using plausible future plan’s normal costs and accrued liabilities under distinct time horizons. Based on the proposed performance measurement, the optimal funding schedule and portfolio selections are determined dynamically without trading restrictions. A private pension scheme is selected and analyzed for numerical illustration. It shows that the optimal contribution rates are between 4.2﹪and 5.1﹪for this specific case. Comparing the funding schedules for distinct time horizons, we find that the contribution rates under 5-year period are higher than those under 10-year period in the beginning. The contribution rates given funding ratio at 75﹪are lower than those given at 100﹪. While the optimal trading behaviors of the pension fund managers for 5-year period are significant volatile than those for 10-year period. Their optimal trading behaviors have exhibited a reduced volatility under the lower funding ratios. The case study indicates that the distinct time horizon and the funding ratio play crucial roles in decision-making process for pension fund management.

本研究以免疫理論（Immunization Theory）與投資組合理論（Portfolio Theory）來架構退休基金的資產負債管理模型，希望在免除利率風險的情況下，極大化退休基金的投資報酬率。本文以退撫基金86年到88年實際投資的實證資料及其對未來給付支出的預測模擬值，在不同考慮年限與提撥率下，建議其最適投資組合，並計算出資產負債管理的成本。最後，再以84年到88年市場平均資料的實證結果，支持並驗證我們以退撫基金內部資料所做的實證結果。研究發現： 1、資產負債管理的成本相當少，因此退撫基金應該儘早進行資產負債管理。若以資產負債管理前後效率前緣下投資報酬率的差異為資產負債管理的成本，以退撫基金內部資料的研究顯示，資產負債管理的平均成本為0.133﹪；以市場平均資料的研究顯示，資產負債管理的平均成本為0.234﹪。 2、在進行資產負債管理的分析後，退撫基金的薪資提撥率應提高至14.84﹪，才能確保未來的30年內，退撫基金不會因為利率變動而導致基金破產甚至無力清償。 3、要使退撫基金免於利率風險的年限愈長，其投資重心必須從短期票券和債券移到債券與股票或受益憑證上。 / This paper investigates the Asset-Liability Management for pension fund. We utilize Immunization Theory and Portfolio Theory selection model to immunize the surplus of pension funds against interest-rate fluctuations and to maximize expected return of pension fund simultaneously. In addition, we use the public trading data of the investment market in Taiwan from 1995 to1999 and the data from the Taiwan Public Employees Retirement System（TPERS）from1997 to 1999 to demonstrate the implementation of our model. We calculate the optimal asset allocation and the ALM cost under different time horizons and contribution rates. The empirical results from this study show that: 1、 The ALM cost is very small. Therefore, we suggest TPERS should start to implement ALM as soon as possible. Given the investment performance of TPERS, We find the ALM cost is 0.133﹪. Given the performance of the investment market, the ALM cost is 0.234﹪. 2、 The TPERS must increase its contribution rate to 14.84﹪ in order to make sure that the TPERS will not be insolvent as a result of interest-rate fluctuations in 30 years. 3、 To prolong the period over which the TPERS can immunize its surplus against interest-rate fluctuations, a large proportion of the investment asset should be allocate from commercial paper and bond to bond and stock.

金融機構之降息政策與全球經濟環境之不確定性，大幅增加人壽保險人之經營風險，以鄰國日本人壽保險為例，自1996年日產生命發生財務危機開始，已有5家保險公司宣佈倒閉或破產，6家進行合併，其餘14家也面臨嚴重之財務壓力，為避免系統風險造成台灣人壽保險產業之破產危機，如何創新保險商品及研擬風險管理成為重要之議題。 　　人壽保險公司之負債資產比極高，因此公司之財務健全與投保人之權益息息相關，利率變動將顯著影響公司獲利能力，因此利率風險管理實為當務之急。投資型商品之開發為人壽保險產業因應利率風險之新興策略，早期為人壽保險與共同基金結合，或與銀行定存結合，近來發展出與指數型金融商品連結之保本型人壽保險。因為商品之複雜度，評價將成為重要之課題，投資型保險基於被保險人參與財務風險程度之大小差異，風險管理與傳統型保險有所差別。 　　本研究首先探討目前人壽保險市場之現況，詳細定義投資型人壽保險，探討發展過程，並實際進行試算與評價分析，列舉說明精算之規範，資產負債管理、風險資本額制度下之定位及外匯等問題，以個案討論台灣及中國大陸市場之投資型商品，並提出現況之建議。 / Due to the monetary policy in the banking sector and the global economic uncertainty, the solvency issue for the life insurer becomes crucial. In Japan life insurance market, five insurers have declared their bankruptcy since 1996, six insurers had been merged, and the others have suffered serious financial press. Preventing the ruin crisis of life insurers and strengthen their financial abilities through innovation products and risk management techniques in Taiwan have become an important issue for the management. 　　Owing to the high leverage ratio in life insurer's capital structure, the reserve adequacy plays a vital role in shielding the policyholder's rights. Since the uncertainty of the interest rate affects the reserve and surplus of the insurer, asset-liability risk management becomes an important subject. Adding the investment-linked life insurance policies in the insurer's liability portfolio is an innovative strategy in managing the low interest risk. Combining with the mutual fund or the bank certificates in early stage has advanced to integrate with the equity indexed products. The investment-linked products vary from the traditional ones allowing the participation in the financial risks. Owing to the complexity of its design, the valuation becomes essential. 　　This study analyzes investment-linked life insurance policies and their historical evolutions. The financial valuation processes are illustrated explicitly. The regulations in the reserve valuation, the asset-liability management, the connection with risk-based capital (RBC) and the related hedging issues are also explored. Finally, the product designs and managerial issues in operating the investment-linked life insurance policies in Taiwan and Mainland China are discussed.

壽險業所販賣之商品通常為長年期保單，此一商品特性使得壽險公司的責任準備金(負債)非常容易受到市場利率波動而產生變動，進而影響到公司的清償能力。因此，資產負債管理對壽險公司來說一直是非常重要的一個課題。 過去的會計制度並未強制要求保險公司在財報中反應出準備金對利率的波動，資產負債管理的好處便無法在這樣的會計制度之下產生原有的作用，進而可能導致保險公司不重視這樣的管理方式。近年來保險監理的國際趨勢致力於加強準備金公平衡量以及真實揭露保險業的負債價值，因此我們可以預期在未來準備金的波動對保險公司的影響會較現在來得顯著，資產負債管理對壽險公司也應該會有較為顯著的影響。 本研究採用模擬的方式，比較不同投資策略的壽險公司在不同會計制度之下的財務狀況，進而探討資產負債管理的策略是否確實能讓保險人在公平價值準備金下較不受利率波動之影響。本研究的結果顯示在公平價值準備金的架構下，採用資產負債管理的壽險公司其損益會較沒採用資產負債管理的壽險公司穩定；若是在帳面價值準備金的架構下，採用資產負債管理的公司反而因為做出了多餘的避險行為致使其損益較不穩定。另外，本研究發現若是保險公司在資產負債策略下所採用的避險指標不符合目前法規，對公司的損益也會造成不必要的波動。因此本研究認為保險公司在實行資產負債管理策略時，應該參照目前會計制度下所給定的方式來做避險，進而達到最大的效益。 / Life insurers' liability value is relatively sensitive to interest rate due to the long term characteristic of the policies. The high leverage ratio strengthens the impact on how interest rate can influence solvency.. Life insurer therefore should manage their assets and liability in a prudent way. In the past, supervisory authorities used to regulate the insurer to recognize their liabilities in book value, which makes the benefits of ALM insignificant. Under such regulation, the main purpose of asset allocation for most of the life insurers was to generate higher investment return instead of matching asset with the liability, nor to maintain risk at acceptable level under book-value reserving. The international financial report standard No.4 (IFRS4) suggests that insurers should measure their liability under fair value in the future. The new regulation may increases the volatility of the life insurer's liability and emerges the benefit of ALM The objective of this article is to compare the effect of ALM strategy on life insurer's financial statement under both accounting standards via simulation methods. The result shows that the insurers with ALM face more stable financial statement if they manage their interest rate decently. One of the results shows that the insurers who manage their asset based on fair value duration faces more volatility than insurers without ALM under book value reserve. This implies that the insurer with ALM still suffers higher volatility if the regulations do not support such behavior. We therefore suggest that the insurers should manage their asset based on their liability interest rate risk under the condition that they choose the appropriate interest rate risk indicator to fit different regulations.