Uppsatsen behandlar begagnade livförsäkringar och de implikationer som dessa kan komma att innebära för den svenska livförsäkringsmarknaden i framtiden. Syftet med uppsatsen är att analysera vinsterna och riskerna med marknaden för begagnade livförsäkringar i Sverige och utifrån detta resultat utvärdera vad reglerare av marknaden måste betänka. I uppsatsen avses med livförsäkringar enbart livförsäkringar med dödsfallsbelopp. Vi visar på hur livförsäkringar traditionellt är uppbyggda och hur livförsäkringspremiernas storlek bestäms. En bakgrund ges till den svenska försäkringsmarknaden och dess grundläggande principer samt den förändring som branschen genomgår och hur denna kan tänkas resultera i att ett större intresse för handel med livförsäkringar uppstår för både försäkrade och investerare. En jämförelse görs med den amerikanska livförsäkringsmarknaden för att få en uppfattning om riktningen som marknadskrafter kan tänkas föra en oreglerad marknad mot. Handeln med begagnade livförsäkringar är där väl utbredd och debatten kring dess konsekvenser för individer och livförsäkringsbranschen är omfattande. Uppsatsen finner att andrahandsmarknaden gör att livförsäkringar som redan tecknats blir en ren finansiell tillgång och att klassiska marknadsinslag som värdepapperisering är en tänkbar utveckling. Situationen i USA visar också att tillåtande av en andrahandsmarknad riskerar att leda till att livförsäkringar tecknas även för individer som inte utnyttjar dessa ur trygghetssynpunkt. Studien utnyttjar amerikansk forskning på området som underlag för vidare diskussion för andrahandsmarknadens konsekvenser. Hälsoförändringars påverkan på det förväntade värdet av ett livförsäkringskontrakt analyseras och de situationer där en försäljning av livförsäkringskontrakt är lönsam för den försäkrade och investerare diskuteras. Uppsatsen tar upp anledningar till att information kan fördelas asymmetriskt mellan aktörer och analyserar vilka konsekvenser detta kan få. Vi finner att bättre kännedom om individens hälsotillstånd leder till större vinster genom andrahandsmarknaden men att aktörer av olika anledningar kan vara förhindrade att utnyttja denna information. Uppsatsen analyserar hur olika aktörer påverkas av andrahandsmarknaden för livförsäkringar. Vi finner att vinnarna är investerare, mellanhänder och de individer som förlorat anledningen att behålla sina livförsäkringskontrakt. Livförsäkringsföretagen förlorar alltid på marknaden. Huruvida försäkringstagarkollektivet som helhet vinner eller förlorar genom andrahandsmarknaden beror på de antaganden som ligger till grund för livförsäkringspremiernas storlek. Marknadens storlek och dess betydelse för transaktionskostnader diskuteras, liksom olika moraliska aspekter av handel med begagnade livförsäkringar. Uppsatsen diskuterar också de samhällsrisker som är förenade med att aktörer kan vinna på individers död. Uppsatsen finner att begagnade livförsäkringar i vissa fall är önskvärt för samhället men att marknaden måste regleras hårt för att förhindra orättvisor och svaga positioner för de försäkrade. Höga kostnader kan uppstå både för reglering och för inhämtande av information för marknadens aktörer. Slutligen lyfter uppsatsen fram ett antal aspekter som reglerare av andrahandsmarknaden för livförsäkringar måste betänka.

This dissertation studies the adverse financial implications of "longevity risk" and "mortality risk", which have attracted the growing attention of insurance companies, annuity providers, pension funds, public policy decision-makers, and investment banks. Securitization of longevity/mortality risk provides insurers and pension funds an effective, low-cost approach to transferring the longevity/mortality risk from their balance sheets to capital markets. The modeling and forecasting of the mortality rate is the key point in pricing mortality-linked securities that facilitates the emergence of liquid markets. First, this dissertation introduces the discrete models proposed in previous literature. The models include: the Lee-Carter Model, the Renshaw Haberman Model, The Currie Model, the Cairns-Blake-Dowd (CBD) Model, the Cox-Lin-Wang (CLW) Model and the Chen-Cox Model. The different models have captured different features of the historical mortality time series and each one has their own advantages. Second, this dissertation introduces a stochastic diffusion model with a double exponential jump diffusion (DEJD) process for mortality time-series and is the first to capture both asymmetric jump features and cohort effect as the underlying reasons for the mortality trends. The DEJD model has the advantage of easy calibration and mathematical tractability. The form of the DEJD model is neat, concise and practical. The DEJD model fits the actual data better than previous stochastic models with or without jumps. To apply the model, the implied risk premium is calculated based on the Swiss Re mortality bond price. The DEJD model is the first to provide a closed-form solution to price the q-forward, which is the standard financial derivative product contingent on the LifeMetrics index for hedging longevity or mortality risk. Finally, the DEJD model is applied in modeling and pricing of life settlement products. A life settlement is a financial transaction in which the owner of a life insurance policy sells an unneeded policy to a third party for more than its cash value and less than its face value. The value of the life settlement product is the expected discounted value of the benefit discounted from the time of death. Since the discount function is convex, it follows by Jensen's Inequality that the expected value of the function of the discounted benefit till random time of death is always greater than the benefit discounted by the expected time of death. So, the pricing method based on only the life expectancy has the negative bias for pricing the life settlement products. I apply the DEJD mortality model using the Whole Life Time Distribution Dynamic Pricing (WLTDDP) method. The WLTDDP method generates a complete life table with the whole distribution of life times instead of using only the expected life time (life expectancy). When a life settlement underwriter's gives an expected life time for the insured, information theory can be used to adjust the DEJD mortality table to obtain a distribution that is consistent with the underwriter projected life expectancy that is as close as possible to the DEJD mortality model. The WLTDDP method, incorporating the underwriter information, provides a more accurate projection and evaluation for the life settlement products. Another advantage of WLTDDP is that it incorporates the effect of dynamic longevity risk changes by using an original life table generated from the DEJD mortality model table. / text

My doctoral thesis “Essays on Lifetime Uncertainty: Models, Applications, and Economic Implications” addresses economic and mathematical aspects pertaining to uncertainties in human lifetimes. More precisely, I commence my research related to life insurance markets in a methodological direction by considering the question of how to forecast aggregate human mortality when risks in the resulting projections is important. I then rely on the developed method to study relevant applied actuarial problems. In a second strand of research, I consider the uncertainty in individual lifetimes and its influence on secondary life insurance market transactions. Longevity risk is becoming increasingly crucial to recognize, model, and monitor for life insurers, pension plans, annuity providers, as well as governments and individuals. One key aspect to managing this risk is correctly forecasting future mortality improvements, and this topic has attracted much attention from academics as well as from practitioners. However, in the existing literature, little attention has been paid to accurately modeling the uncertainties associated with the obtained forecasts, albeit having appropriate estimates for the risk in mortality projections, i.e. identifying the transiency of different random sources affecting the projections, is important for many applications. My first essay “Coherent Modeling of the Risk in Mortality Projections: A Semi-Parametric Approach” deals with stochastically forecasting mortality. In contrast to previous approaches, I present the first data-driven method that focuses attention on uncertainties in mortality projections rather than uncertainties in realized mortality rates. Specifically, I analyze time series of mortality forecasts generated from arbitrary but fixed forecasting methodologies and historic mortality data sets. Building on the financial literature on term structure modeling, I adopt a semi-parametric representation that encompasses all models with transitions parameterized by a Normal distributed random vector to identify and estimate suitable specifications. I find that one to two random factors appear sufficient to capture most of the variation within all of our data sets. Moreover, I observe similar systematic shapes for their volatility components, despite stemming from different forecasting methods and/or different mortality data sets. I further propose and estimate a model variant that guarantees a non-negative process of the spot force of mortality. Hence, the resulting forward mortality factor models present parsimonious and tractable alternatives to the popular methods in situations where the appraisal of risks within medium or long-term mortality projections plays a dominant role. Relying on a simple version of the derived forward mortality factor models, I take a closer look at their applications in the actuarial context in the second essay “Applications of Forward Mortality Factor Models in Life Insurance Practice. In the first application, I derive the Economic Capital for a stylized UK life insurance company offering traditional product lines. My numerical results illustrate that (systematic) mortality risk plays an important role for a life insurer's solvency. In the second application, I discuss the valuation of different common mortality-contingent embedded options within life insurance contracts. Specifically, I present a closed-form valuation formula for Guaranteed Annuity Options within traditional endowment policies, and I demonstrate how to derive the fair option fee for a Guaranteed Minimum Income Benefit within a Variable Annuity Contract based on Monte Carlo simulations. Overall my results exhibit the advantages of forward mortality factor models in terms of their simplicity and compatibility with classical life contingencies theory. The second major part of my doctoral thesis concerns the so-called life settlement market, i.e. the secondary market for life insurance policies. Evolving from so-called “viatical settlements” popular in the late 1980s that targeted severely ill life insurance policyholders, life settlements generally involve senior insureds with below average life expectancies. Within such a transaction, both the liability of future contingent premiums and the benefits of a life insurance contract are transferred from the policyholder to a life settlement company, which may further securitize a bundle of these contracts in the capital market. One interesting and puzzling observation is that although life settlements are advertised as a high-return investment with a low “Beta”, the actual market systematically underperformed relative to expectations. While the common explanation in the literature for this gap between anticipated and realized returns falls on the allegedly meager quality of the underlying life expectancy estimates, my third essay “Coherent Pricing of Life Settlements under Asymmetric Information” proposes a different viewpoint: The discrepancy may be explained by adverse selection. Specifically, by assuming information with respect to policyholders’ health states is asymmetric, my model shows that a discrepancy naturally arises in a competitive market when the decision to settle is taken into account for pricing the life settlement transaction, since the life settlement company needs to shift its pricing schedule in order to balance expected profits. I derive practically applicable pricing formulas that account for the policyholder’s decision to settle, and my numerical results reconfirm that---depending on the parameter choices---the impact of asymmetric information on pricing may be considerable. Hence, my results reveal a new angle on the financial analysis of life settlements due to asymmetric information. Hence, all in all, my thesis includes two distinct research strands that both analyze certain economic risks associated with the uncertainty of individuals’ lifetimes---the first at the aggregate level and the second at the individual level. My work contributes to the literature by providing both new insights about how to incorporate lifetime uncertainty into economic models, and new insights about what repercussions---that are in part rather unexpected---this risk factor may have.

In this study a methodological approach is presented on how transactions in the secondary market for life insurance policies can be fairly priced for both policyholders and life settlement companies. Monte Carlo simulation of mortality on a pool constructed based on actual data of 85 life settlement transactions shows that a realistic assumption for the range of offered prices is limited to 15% and 20% of the face amount of the policy, given a required return of 7%. The power of the proffered pricing approach is ensured by assessing and managing mortality risk along with the other pertinent risks using stress testing, where mortality risk appears to be analogous to some extent with systematic risk on other markets of assets.

The Lee-Carter mortality model provides the very first model for modeling the mortality rate with stochastic time and age mortality dynamics. The model is constructed modeling the mortality rate to incorporate both an age effect and a period effect. The Lee-Carter model provides the fundamental set up currently used in most modern mortality modeling. Various extensions of the Lee-Carter model include either adding an extra term for a cohort effect or imposing a stochastic process for mortality dynamics. Although both of these extensions can provide good estimation results for the mortality rate, applying them for the pricing of the mortality/ longevity linked derivatives is not easy. While the current stochastic mortality models are too complicated to be explained and to be implemented, transforming the cohort effect into a stochastic process for the pricing purpose is very difficult. Furthermore, the cohort effect itself sometimes may not be significant. We propose using a new modified Lee-Carter model with a Normal Inverse Gaussian (NIG) Lévy process along with the Esscher transform for the pricing of mortality/ longevity linked derivatives. The modified Lee-Carter model, which applies the Lee-Carter model on the growth rate of mortality rates rather than the level of mortality rates themselves, performs better than the current mortality rate models shown in Mitchell et al (2013). We show that the modified Lee-Carter model also retains a similar stochastic structure to the Lee-Carter model, so it is easy to demonstrate the implication of the model. We proposed the additional NIG Lévy process with Esscher transform assumption that can improve the fit and prediction results by adapting the mortality improvement rate. The resulting mortality rate matches the observed pattern that the mortality rate has been improving due to the advancing development of technology and improvements in the medical care system. The resulting mortality rate is also developed under a martingale measure so it is ready for the direct application of pricing the mortality/longevity linked derivatives, such as q-forward, longevity bond, and mortality catastrophe bond. We also apply our proposed model along with an information theoretic optimization method to construct the pricing procedures for a life settlement. While our proposed model can improve the mortality rate estimation, the application of information theory allows us to incorporate the private health information of a specific policy holder and hence customize the distribution of the death year distribution for the policy holder so as to price the life settlement. The resulting risk premium is close to the practical understanding in the life settlement market.