Description: It is obvious that the introduction of a deductible has two major effects. The amount paid for every claim will drop, resulting in a lower claim burden for the insurance company. There will also be a drop in claim frequency, leading to a decrease in claim handling expenses. However, it is by no means obvious how the average claim size changes with the introduction of a deductible. In this paper, we will study this question. First, we derive some theoretical results then apply them to concrete distributions.

Description: This is a Fellowship Credit Research Paper. A portfolio of different insurance policies such as temporary, endowment and whole-life insurance policies is studied in a stochastic mortality and interest environment. The first two moments of the present value of the benefits of the portfolio are derived. The riskiness of the portfolio as measured by the variance of the present value of the benefits can be divided into an insurance risk and an investment risk in two different ways. One way leads to a more natural interpretation of the two risk components. A simple portfolio is used to illustrate the results.

Description: This note develops the optimality of the put option as a hedging strategy. For an investor who owns a stock, he can buy a put option to hedge against the downside risk of the stock price. In this short note, we ask two questions with the hedge strategy of the put option. First, whether the investor is better off with the hedging strategy? Second, if the investor is better off with the hedging strategy, whether it is the optimal hedging plan? Our result shows that in a risk averse world an investor will maximize his utility with buying the put option as a hedge strategy.

Description: The investment risk generated by a stochastic interest rate is recognized as often the greatest risk associated with a whole life or retirement policy. Recent research has investigated the mathematics of this risk when the interest rate follows a stochastic process and the time to death is considered to be random. In this paper we focus on the use of the zero coupon bond as an investment instrument to fund a whole life policy. It is unlikely that a company will entirely fund a particular single policy with a zero coupon bond.

Description: This paper examines the problem of hedging foreign exchange risk across multiple countries using currency options. The profit target requirement is formulated as a stochastic constraint in the context of a binomial lattice. Models are presented for European options. In a numerical example, five currency options are selected, allowing for long or short positions, depending on the target value.

Description: In this paper we discuss the link between the price of a contingent claim and its replicating strategies. We compute the replicating strategies for some contingent claims when the price of stocks are modeled using either the Wiener process or the Poisson process. These replicating strategies are essential knowledge if one wishes to implement a dynamic trading strategy.