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.

Following a recent strand of literature, in order to gain insights on what drives policyholder behavior, I first develop a life-cycle model for variable annuities (VA) with withdrawal guarantees. However, I explicitly allow for outside savings and investments, which considerably affects the results. Specifically, I find that withdrawal patterns after all are primarily motivated by value maximization – but with the important asterisk that the value maximization should be taken out from the policyholders’ perspective accounting for individual tax benefits.

To this effect, I develop a risk-neutral valuation methodology that takes these different tax structures into consideration, and apply it to our example contract as well as a representative empirical VA. The results are in line with corresponding outcomes from the life cycle model, and I find that the withdrawal guarantee fee from the empirical product roughly accords with its marginal price to the insurer.

I further consider the implications of policyholder behavior on product design. In particular – due to differential tax treatments and contrary to option pricing theory – the marginal value of such guarantees can become negative, even when the holder is a value maximizer. For instance, as I illustrate with both a simple two-period model and an empirical VA, a common death benefit guarantee may indeed yield a negative marginal value to the insurer.

In Chapter 1, we develop a dynamic model to examine the effects of asymmetric beliefs of a firm's manager and blockholders regarding the profitability of the firm's projects, and differing attitudes towards their risk, on its capital structure. The firm's capital structure reflects the tradeoff between the positive incentive effects of managerial optimism that increases the manager's output and blockholders' private benefits against the negative effects of risk-sharing costs. We provide several testable implications for the effects of the degree of managerial optimism as well as permanent and transitory components of the firm's risk on different components of capital structure. In our calibration of the model, performed separately for different industries, we show that while optimism and risk have qualitatively similar effects on capital structure in different industries, their quantitative effects are significantly different. The interactive effects of asymmetric beliefs and agency conflicts could potentially explain a significant portion of the substantial inter-industry variation in capital structure.

Chapter 2 studies how the distributions of CEO talent and compensation vary across industries, and how product market characteristics affect these distributions. We develop a market equilibrium model that incorporates the competitive assignment of CEOs to firms in a framework in which firms engage in imperfect product market---specifically, monopolistic---competition. Using the distributions of CEO pay and firm value in each of twelve Fama-French industries, we calibrate the parameters of our structural model, and indirectly infer the unobserved distributions of CEO talent and firm quality that together determine firm output. We then conduct several counterfactual experiments using the calibrated models corresponding to each of the industries. We find that the distribution of CEO talent does, indeed, vary dramatically across industries. More importantly, contrary to the conclusions of earlier studies that abstract away from the effects of the product market (Tervio, 2008 and Gabaix and Landier, 2008), the impact of CEO talent on firm value appears to be quite significant. Our estimates of the effect of CEO talent on firm value for the industries in our sample are two orders of magnitude higher than those obtained by the aforementioned studies. Further, our estimates suggest that the compensation of CEOs is quantitatively in line with their contributions to firms. Broadly, our study shows that it is important to incorporate the product market environment in which firms operate when assessing the contributions of CEOs to firms.

Chapter 3 builds a market equilibrium framework in which the CEO-firm matching process is affected by the product market. We show that under reasonable assumptions there is a unique equilibrium in which only managers with ability above a unique cutoff level are matched to firms. This very simple screening process endogenizes the distribution of active managers who match with firms. Our calibration of the model using a parametric approach, which is in contrast with the empirical analysis performed in Chapter 2, strongly supports the principle arguments on the importance of CEO talent and appropriate CEO talent levels (on average) in Chapter 2. In addition, due to the law of demand and supply, which is a key feature of the extended model, we obtain somewhat different influence of some of product market characteristics on CEO pay. Furthermore, our parametric approach allows us to draw some implications for the effects of CEO talent distribution on the market equilibrium.

To address the issue of soaring property insurance premiums and coverage availability in states that are subject to hurricane risks, state and federal governments have not only regulated the private insurance market but have also intervened directly into markets by establishing government-funded insurance programs. With coexisting public and private insurance mechanisms and price regulation, the risk of cross subsidization and a subsequent moral hazard problem may arise. By using data from the Florida Citizens Insurance Corporation, the Florida Hurricane Catastrophe Fund, the Flood Insurance and the private homeowner insurance market in Florida from 1998 to 2007, the second essay examines the moral hazard problems arising from government regulation and involvement in the private insurance sector. In sum, the provision of national flood insurance is found to be positively related to the population growth in the state of Florida, which shows that state immigrants can take advantage of the lower cost of flood insurance when relocating in higher-risk areas. Further, we find that national flood insurance and the catastrophe fund complement the development of the private insurance sector, while the residual market hinders the development of private property insurance market.