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<p>Hip fractures are the most serious consequence of osteoporosis, and are one important cause of morbidity and mortality among the elderly. Prophylactic treatment for hip fractures are now available. Early detection of individuals with increased risk for hip fractures is therefor of great interest. A subset of non-institutionalised patients with a first hip fracture (cases;n=l18) and controls (n=263), aged 65-85 years, underwent dual X-ray absorptiometry (DXA) of the femoral neck, quantitative ultrasound (QUS) of the heel and phalanges and radiographic absorptiometry (RA) of the phalanges. The entire cohort was followed for approximately four years or to death. In women, DXA of the proximal femur and QUS of the heel showed a high predictive value for an incident first hip fracture, adjusted odds ratio (OR) 3.6 (95% confidence interval (CI) 2.4-5.5) and 3.4 (95%CI 2.2-5.0) respectively. The association was even stronger in men, but only for DXA of the proximal femu,r with an adjusted OR of4.8 (95%CI 2.3-9.9). Bone densitometry at non-weight-bearing sites, QUS and RA of the phalanges did not discriminate female cases from controls, but proved capable of separating male cases from controls. The risk of death was higher in cases than in controls, with a multivariate rate ratio (RR) of 3.4 (95%CI 1.7-7.0). There was no significant association between bone density and mortality. </p><p>Nursing home residents underwent QUS of the heel and phalanges. Almost all of the female residents and 51% of the male residents were, if the WHO-criterion for osteoporosis was applied, osteoporotic as assessed by heel and finger QUS. The QUS values were approximately 1.5 SD lower than expected for age and gender. </p><p>In this randomised controlled intervention study we evaluated the effect of external hip protectors in nursing home residents; 302 residents were allocated to wear such protectors and 442 were controls. External hip protectors were found to be effective in preventing hip fractures in nursing home residents, with an adjusted relative risk for hip fracture of 0.33 (CI 0.11 - 1.00). </p>

Hip fractures are the most serious consequence of osteoporosis, and are one important cause of morbidity and mortality among the elderly. Prophylactic treatment for hip fractures are now available. Early detection of individuals with increased risk for hip fractures is therefor of great interest. A subset of non-institutionalised patients with a first hip fracture (cases;n=l18) and controls (n=263), aged 65-85 years, underwent dual X-ray absorptiometry (DXA) of the femoral neck, quantitative ultrasound (QUS) of the heel and phalanges and radiographic absorptiometry (RA) of the phalanges. The entire cohort was followed for approximately four years or to death. In women, DXA of the proximal femur and QUS of the heel showed a high predictive value for an incident first hip fracture, adjusted odds ratio (OR) 3.6 (95% confidence interval (CI) 2.4-5.5) and 3.4 (95%CI 2.2-5.0) respectively. The association was even stronger in men, but only for DXA of the proximal femu,r with an adjusted OR of4.8 (95%CI 2.3-9.9). Bone densitometry at non-weight-bearing sites, QUS and RA of the phalanges did not discriminate female cases from controls, but proved capable of separating male cases from controls. The risk of death was higher in cases than in controls, with a multivariate rate ratio (RR) of 3.4 (95%CI 1.7-7.0). There was no significant association between bone density and mortality. Nursing home residents underwent QUS of the heel and phalanges. Almost all of the female residents and 51% of the male residents were, if the WHO-criterion for osteoporosis was applied, osteoporotic as assessed by heel and finger QUS. The QUS values were approximately 1.5 SD lower than expected for age and gender. In this randomised controlled intervention study we evaluated the effect of external hip protectors in nursing home residents; 302 residents were allocated to wear such protectors and 442 were controls. External hip protectors were found to be effective in preventing hip fractures in nursing home residents, with an adjusted relative risk for hip fracture of 0.33 (CI 0.11 - 1.00).

This thesis aims at contributing to the study of the valuation of insurance liabilities and the management of the assets backing these liabilities. It consists of four parts, each devoted to a specific topic. In the first part, we study the pricing of a classical single premium life insurance contract with profit, in terms of a guaranteed rate on the premium and a participation rate on the (terminal) financial surplus. We argue that, given the asset allocation of the insurer, these technical parameters should be determined by taking explicitly into account the risk management policy of the insurance company, in terms of a risk measure such as the value-at-risk or the conditional value-at-risk. We then design a methodology that allows us to fix both parameters in such a way that the contract is fairly priced and simultaneously exhibits a risk consistent with the risk management policy. In the second part, we focus on the management of the surrender option embedded in most life insurance contracts. In Chapter 2, we argue that we should model the surrender time as a random time not adapted to the filtration generated by the financial assets prices, instead of assuming that the surrender time is an optimal stopping time as it is usual in the actuarial literature. We then study the valuation of insurance contracts with a surrender option in such a model. We here follow the financial literature on the default risk and in particular, the reduced-form models. In Chapter 3 and 4, we study the hedging strategies of such insurance contracts. In Chapter 3, we study their risk-minimizing strategies and in Chapter 4, we focus on their ``locally risk-minimizing' strategies. As a by-product, we study the impact of a progressive enlargement of filtration on the so-called ``minimal martingale measure'. The third part is devoted to the systematic mortality risk. Due to its systematic nature, this risk cannot be diversified through increasing the size of the portfolio. It is thus also important to study the hedging strategies an insurer should follow to mitigate its exposure to this risk. In Chapter 5, we study the risk-minimizing strategies for a life insurance contract when no mortality-linked financial assets are traded on the financial market. We here extend Dahl and Moller’s results and show that the risk-minimizing strategy of a life insurance contract is given by a weighted average of risk-minimizing strategies of purely financial claims, where the weights are given by the (stochastic) survival probabilities. In Chapter 6, we first study the application of the HJM methodology to the modelling of a longevity bonds market and describe a coherent theoretical setting in which we can properly define the longevity bond prices. Then, we study the risk-minimizing strategies for pure endowments and annuities portfolios when these longevity bonds are traded. Finally, the fourth part deals with the design of ALM strategies for a non-life insurance portfolio. In particular, this chapter aims at studying the risk-minimizing strategies for a non life insurance company when inflation risk and interest rate risk are taken into account. We derive the general form of these strategies when the cumulative payments of the insurer are described by an arbitrary increasing process adapted to the natural filtration of a general marked point process and when the inflation and the term structure of interest rates are simultaneously described by the HJM model of Jarrow and Yildirim. We then systematically apply this result to four specific models of insurance claims. We first study two ``collective' models. We then study two ``individual' models where the claims are notified at a random time and settled through time.

<p>Under det gångna århundradet ökade den förväntade livslängden avsevärt såväl i Sverige som i övriga världen. 1900-talets förbättrade livslängd drevs inledningsvis av en minskad barnadödlighet medan de senare årtiondena kännetecknades av minskad dödlighet i höga åldrar.</p><p>En åldrande befolkning innebär ökade krav på sjukvård, äldreomsorg och inte minst pensionssystem. Pålitliga prognoser för vår framtida livslängd behövs för att beräkna de resurser som nämnda verksamheter kommer att ta i anspråk och utgör förutsättningen för en rättvis prissättning av försäkringsprodukter med levnadsrisk.</p><p>Lee-Carter-modellen är en av vår tids tongivande modeller för mortalitetsprognostisering. Modellen används här för att göra livslängdsprognoser utifrån svenska mortalitetsdata; prognoserna jämförs sedan med observerade utfall.</p><p>Mot bakgrund av resultatet diskuteras levnadsrisk med fokus på pensioner.</p><p>Inte oväntat presterar prognoserna ingen felfri bild av verkligheten och prognosfelet varierar i storlek mellan skattningarna; att använda dem som underlag för pensionsberäkningar hade i förlängningen varit ohållbart. Exemplet illustrerar på samma gång vår osäkerhet inför framtidens livslängdsutveckling och svårigheten i att prognostisera den.</p> / <p>During the past century, Sweden along with many other countries experienced a sharp decline in mortality rates. The increased life expectancy was initially propelled by mortality reductions among infants and subsequently by a survival improvement in advanced ages.</p><p>An ageing population has large implications for those providing services to the elderly, such as medical care and pensions, whilst also addressing the need for accurate and reliable mortality forecasts and projection methods.</p><p>The Lee-Carter model is the current gold standard for mortality forecasting and has been widely adopted in several studies. Here, the model is applied on Swedish mortality data; the projections are then compared to the observed lifespan development. Against this backdrop, a discussion on longevity risk in pensions schemes follows.</p><p>The forecasts performed in this study do not perfectly reflect the observed mortality change in the examined period; furthermore, the variation of the estimation errors limits the actuarial value of the projections. The findings illuminate the uncertainty that surrounds our future life expectancy as well as the difficulties associated with forecasting it.</p>

<p>Osteoporosis is a major health care problem, by reason of its devastating consequences, in particular hip fractures. Worldwide it has been estimated that the incidence of hip fracture will increase to more than 6 million per year by 2050 compared to 1.7 million per year in 1990. Osteoporosis can be caused by various factors namely, genetic, lifestyle and environmental factors, and since the rising incidence of its consequences is not fully explained by the growing age of the population, there is an urgent need to identify individual causal factors of this condition. </p><p>The present research has focused on aluminium, one potential environmental factor of importance for bone disease, and its possible relation to osteoporosis, since it is known to cause osteoporosis-like bone disease and has been associated with induction of progressive central nervous system diseases.</p><p>Aluminium is the third most common element in the earth’s crust and the most abundant metal (8%). It is widely utilized industrially and it is also naturally present in many foods. Although aluminium is ubiquitous in the human environment, evolution has not given it an essential biological function.</p><p>The aluminium content of bone was measured by inductively coupled mass spectrometry in a large group of patients suffering from hip fractures, high energy fractures and osteoarthrosis. An exponential increase in aluminium content of bone with age was found (p=0.0004). However, no significant association of aluminium in bone with occurrence of hip fracture or dementia could be found, and no indirect evidence was obtained, e.g. through bone mineral density or biomechanical properties, that aluminium is involved in the pathogenesis of osteoporosis. Although we accumulate aluminium in bone throughout our lives, and there are experimental suggestions that aluminium induces premature cell death, the body content of this metal does not seem to influence the overall mortality risk. </p>

Osteoporosis is a major health care problem, by reason of its devastating consequences, in particular hip fractures. Worldwide it has been estimated that the incidence of hip fracture will increase to more than 6 million per year by 2050 compared to 1.7 million per year in 1990. Osteoporosis can be caused by various factors namely, genetic, lifestyle and environmental factors, and since the rising incidence of its consequences is not fully explained by the growing age of the population, there is an urgent need to identify individual causal factors of this condition. The present research has focused on aluminium, one potential environmental factor of importance for bone disease, and its possible relation to osteoporosis, since it is known to cause osteoporosis-like bone disease and has been associated with induction of progressive central nervous system diseases. Aluminium is the third most common element in the earth’s crust and the most abundant metal (8%). It is widely utilized industrially and it is also naturally present in many foods. Although aluminium is ubiquitous in the human environment, evolution has not given it an essential biological function. The aluminium content of bone was measured by inductively coupled mass spectrometry in a large group of patients suffering from hip fractures, high energy fractures and osteoarthrosis. An exponential increase in aluminium content of bone with age was found (p=0.0004). However, no significant association of aluminium in bone with occurrence of hip fracture or dementia could be found, and no indirect evidence was obtained, e.g. through bone mineral density or biomechanical properties, that aluminium is involved in the pathogenesis of osteoporosis. Although we accumulate aluminium in bone throughout our lives, and there are experimental suggestions that aluminium induces premature cell death, the body content of this metal does not seem to influence the overall mortality risk.

Under det gångna århundradet ökade den förväntade livslängden avsevärt såväl i Sverige som i övriga världen. 1900-talets förbättrade livslängd drevs inledningsvis av en minskad barnadödlighet medan de senare årtiondena kännetecknades av minskad dödlighet i höga åldrar. En åldrande befolkning innebär ökade krav på sjukvård, äldreomsorg och inte minst pensionssystem. Pålitliga prognoser för vår framtida livslängd behövs för att beräkna de resurser som nämnda verksamheter kommer att ta i anspråk och utgör förutsättningen för en rättvis prissättning av försäkringsprodukter med levnadsrisk. Lee-Carter-modellen är en av vår tids tongivande modeller för mortalitetsprognostisering. Modellen används här för att göra livslängdsprognoser utifrån svenska mortalitetsdata; prognoserna jämförs sedan med observerade utfall. Mot bakgrund av resultatet diskuteras levnadsrisk med fokus på pensioner. Inte oväntat presterar prognoserna ingen felfri bild av verkligheten och prognosfelet varierar i storlek mellan skattningarna; att använda dem som underlag för pensionsberäkningar hade i förlängningen varit ohållbart. Exemplet illustrerar på samma gång vår osäkerhet inför framtidens livslängdsutveckling och svårigheten i att prognostisera den. / During the past century, Sweden along with many other countries experienced a sharp decline in mortality rates. The increased life expectancy was initially propelled by mortality reductions among infants and subsequently by a survival improvement in advanced ages. An ageing population has large implications for those providing services to the elderly, such as medical care and pensions, whilst also addressing the need for accurate and reliable mortality forecasts and projection methods. The Lee-Carter model is the current gold standard for mortality forecasting and has been widely adopted in several studies. Here, the model is applied on Swedish mortality data; the projections are then compared to the observed lifespan development. Against this backdrop, a discussion on longevity risk in pensions schemes follows. The forecasts performed in this study do not perfectly reflect the observed mortality change in the examined period; furthermore, the variation of the estimation errors limits the actuarial value of the projections. The findings illuminate the uncertainty that surrounds our future life expectancy as well as the difficulties associated with forecasting it.

This thesis addresses the absence of explicit pricing formulae and the complexity of proposed models (incomplete markets framework) in the area of mortality risk management requiring the application of advanced techniques from the realm of Financial Mathematics and Actuarial Science. In fact, this is a multi-essay dissertation contributing in the direction of designing and pricing mortality-linked derivatives and offering the state of art solutions to manage longevity risk. The first essay investigates the valuation of Catastrophic Mortality Bonds and, in particular, the case of the Swiss Re Mortality Bond 2003 as a primary example of this class of assets. This bond was the first Catastrophic Mortality Bond to be launched in the market and encapsulates the behaviour of a well-defined mortality index to generate payoffs for bondholders. Pricing this type of bond is a challenging task and no closed form solution exists in the literature. In my approach, we adapt the payoff of such a bond in terms of the payoff of an Asian put option and present a new methodology to derive model-independent bounds for catastrophic mortality bonds by exploiting the theory of comonotonicity. While managing catastrophic mortality risk is an upheaval task for insurers and re-insurers, the insurance industry is facing an even bigger challenge - the challenge of coping up with increased life expectancy. The recent years have witnessed unprecedented changes in mortality rate. As a result academicians and practitioners have started treating mortality in a stochastic manner. Moreover, the assumption of independence between mortality and interest rate has now been replaced by the observation that there is indeed a correlation between the two rates. Therefore, my second essay studies valuation of Guaranteed Annuity Options (GAOs) under the most generalized modeling framework where both interest rate and mortality risk are stochastic and correlated. Pricing these types of options in the correlated environment is an arduous task and a closed form solution is non-existent. In my approach, I employ the use of doubly stochastic stopping times to incorporate the randomness about the time of death and employ a suitable change of measure to facilitate the valuation of survival benefit, there by adapting the payoff of the GAO in terms of the payoff of a basket call option. I then derive general price bounds for GAOs by employing the theory of comonotonicity and the Rogers-Shi (Rogers and Shi, 1995) approach. Moreover, I suggest some `model-robust' tight bounds based on the moment generating function (m.g.f.) and characteristic function (c.f.) under the affine set up. The strength of these bounds is their computational speed which makes them indispensable for annuity providers who rely heavily on Monte Carlo simulations to calculate the fair market value of Guaranteed Annuity Options. In fact, sans Monte Carlo, the academic literature does not offer any solution for the pricing of the GAOs. I illustrate the performance of the bounds for a variety of affine processes governing the evolution of mortality and the interest rate by comparing them with the benchmark Monte Carlo estimates. Through my work, I have been able to express the payoffs of two well known modern mortality products in terms of payoffs of financial derivatives, there by filling the gaps in the literature and offering state of art techniques for pricing of these sophisticated instruments.

本篇論文主要討論在死亡率改善不確定性之下的避險策略。當保險公司負債面的人壽保單是比年金商品來得多的時候，公司會處於死亡率的風險之下。我們假設死亡率和利率都是隨機的情況，部分的死亡率風險可以經由自然避險而消除，而剩下的死亡率風險和利率風險則由零息債券和保單貼現商品來達到最適避險效果。我們考慮mean variance、VaR和CTE當成目標函數時的避險策略，其中在mean variance的最適避險策略可以導出公式解。由數值結果我們可以得知保單貼現的確是死亡率風險的有效避險工具。 / This paper proposes hedging strategies to deal with the uncertainty of mortality improvement. When insurance company has more life insurance contracts than annuities in the liability, it will be under the exposure of mortality risk. We assume both mortality and interest rate risk are stochastic. Part of mortality risk is eliminated by natural hedging and the remaining mortality risk and interest rate risk will be optimally hedged by zero coupon bond and life settlement contract. We consider the hedging strategies with objective functions of mean variance, value at risk and conditional tail expectation. The closed-form optimal hedging formula for mean variance assumption is derived, and the numerical result show the life settlement is indeed a effective hedging instrument against mortality risk.