An equity-linked life insurance contract combines an endowment life insurance and an investment strategy with a minimum guarantee. The benefit of this contract is determined by the guaranteed amount plus a bonus equal to a call on the portfolio. This bonus is similar to an Asian option. We analyze the relationship between the periodic insurance premium and its proportional share invested into the portfolio. For a general model of the financial risks we show the existence and uniqueness of an insurance premium. Furthermore the premium is strictly increasing and convex as a function of the share invested.

A valuation model for equity-linked life insurance contracts incorporating stochastic interest rates is presented. Our model generalizes some previous pricing results of Aase and Persson (1994) and Ekern and Persson (1996), based on deterministic interest rates. Moreover, a design of a new equity-linked product with some appealing features is proposed and compared with the periodical premium contract of Brennan and Schwartz (1976). Our new product is very simple to price and may easily be hedged either by long positions in the mutual fund of linkage or by European call options on the same fund.

Equity-linked life insurance contracts are a type of investment product issued by insurance companies to provide the insured with more appealing benefits, compared with the traditional insurance policy. Such benefits are not only linked to the performance of the underlying investments in the financial market, but also related with some insurance type events, such as death and survival to the contract maturity. Therefore, the equity-linked life insurance contract includes both the financial risk generated from the performance of the risky assets and the insurance risk reflected by the policyholders' survival probability. In this thesis, we consider the problem of utilizing imperfect hedging techniques to value equity-linked life insurance contract with market restrictions: stochastic interest rate and transaction costs. We employ two powerful imperfect hedging techniques to investigate the problem - quantile hedging and efficient hedging. We show that they are effective tools for managing both financial and insurance risk inherent in equity-linked life insurance contracts in a stochastic interest rate economy. Moreover, we incorporate transaction costs in the analysis of quantile hedging on equity-linked life insurance contract. In chapter 2 and chapter 3, we hedge a single premium equity-linked life insurance contract with a stochastic guarantee from quantile and efficient hedging with a stochastic interest rate respectively. We present the explicit theoretical results for the premium of a contract paying the maximum of two risky asset values at maturity, providing the insured can survive to this date. These results allow the straightforward calculation of survival probabilities for the contract owner, which can quantify the insurance companies' mortality risk and target their potential clients. Meanwhile, the numerical examples illustrate the corresponding risk management strategies for insurance companies by applying quantile and efficient hedging. Chapter 4 analyzes the application of quantile hedging on equity-linked life insurance contracts in the presence of transaction costs. We obtain the explicit expressions for the expected present values of hedging errors and transaction costs. Furthermore, the estimated expected present values of hedging errors, transaction costs and total hedging costs are also computed from a simulation approach to compare with the theoretical ones. Finally, the quantile hedging costs of the contract's maturity guarantee inclusive of transaction costs are discussed.

Assuming constant interest rate Brennan and Schwartz (1976, 1979) obtained the rational insurance premium on an equity linked insurance contract through the application of the theory of contingent claim spricing. Further considerations with deterministic interest rate have been discussed in Aase and Persson (1992) and in Persson (1993). Analysing the single premium case Bacinello and Ortu allow for the short term interest rate to develop in accordance to an Ornstein Uhlenbeck process. In a paper from (1994) they consider extentions to both the single and the periodic premium model.This paper presents a model similar to the one by Bacinello and Ortu for the periodic premium case with stochastic interest rate dynamics. It is shown that the insurance contract includes an Asian like option contract. Sufficient conditions on the guaranteed amount for the existence of a solution are derived. As no closed form solution will be obtained we discuss different numerical approaches and apply Monte Carlo simulations with a variance reduction technique.

An equity linked life and pension insurance consists of a non-linear combination of a life and pension insurance with an investment strategy. In addition to the guaranteed payments the insured receives a bonus depending on the value of an investment strategy. The additional payment is similar to an Asian type option. Since the insurance contract combines mortality and financial risks in a non-linear way, the value or premium of the contract must reflect these uncertainties. Within this context a premium sequence is called fair if the accumulated expected discounted premium is equal to the accumulated expected discounted payments of the contract. This paper shows the existence of a fair periodic premium. For two different pension policies an approximation of the fair periodic premium is derived.

A comprehensive guide to investment guarantees in equity-linked life insurance Due to the convergence of financial and insurance markets, new forms of investment guarantees are emerging which require financial service professionals to become savvier in modeling and risk management. With chapters that discuss stock return models, dynamic hedging, risk measures, Markov Chain Monte Carlo estimation, and much more, this one-stop reference contains the valuable insights and proven techniques that will allow readers to better understand the theory and practice of investment guarantees and equity-linked insurance policies. Mary Hardy, PhD (Waterloo, Ontario, Canada), is an Associate Professor and Associate Chair of Actuarial Science at the University of Waterloo and is a Fellow of the Institute of Actuaries and an Associate of the Society of Actuaries, where she is a frequent speaker. Her research covers topics in life insurance solvency and risk management, with particular emphasis on equity-linked insurance. Hardy is an Associate Editor of the North American Actuarial Journal and the ASTIN Bulletin and is a Deputy Editor of the British Actuarial Journal.