Description: This article examines how parameter uncertainty leads to uncertainty in Value at Risk VaR estimates. Lacking a closed form solution, we use a first order approximation of VaR to map parameter changes into changes in the VaR value. When the asymptotic distribution of parameter estimates is normal, this implies a normal approximation of the confidence interval about VaR. We describe this approximation in detail and explore some extensions to risk factor modeling.

Description: This paper presents the modeling of mortality risk from exposure to a potential future extreme event such as a natural disaster and a terrorist attack, and its impact on life insurance. With this new model, quantities associated with the total force of mortality such as survival function are derived and the impact of mortality risk on life insurance is examined.

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 paper demonstrates that using a conditional probability approach to analyzing investment data yields investment forecast and stock option pricing models which more closely match actual market data, and it demonstrates the impact that conditional probabilities could have on CAPM beta and risk premia calculations. Reprinted from: Journal of Financial and Economic Practice, Vol. 6 No. 2 Spring 2006.

Description: This paper discusses the actuarial risk measures and uses a variety of estimation techniques such as nonparametric approach, parametric methods and robust procedures. From 39th Actuarial Research Conference, Iowa City, Iowa, August 5-7, 2004.

Description: Recently, there has been growing interest among insurance and investment experts to focus on the use of a tail conditional expectation as a measure of risk, since it shares properties that are considered desirable and applicable in a variety of situations. This paper examines above risk measure in the case of a multivariate gamma portfolio. We demonstrate the explicit formulas for tail conditional expectation and based on it capital allocation when the proposed multivariate model consists of dependent and independent gamma marginals

Description: This paper investigates the optimal multi-period proportional reinsurance strategy that minimizes the ruin probability of an insurer. Some conditions under which it is optimal to have no reinsurance are derived. Based on these results, a new concept, capital threshold of proportional reinsurance, is introduced. In the case of two periods, a lower bound of the capital threshold of proportional reinsurance is provided. Some economic implications and properties of this new concept are also discussed.

Description: The article provides a complete and rigorous analysis based on calculus for the topics in the theory of compound interest: the monotone convergence properties of the rates of interest and discount payable m times per interest conversion period in relation to the force of interest, the monotone convergence properties of the present value and accumulated value of an ordinary annuity with m payments per interest conversion period in relation to those of a continuously paying ordinary annuity and a method for approximating the present value of an ordinary annuity, or an increasing annuity with m payments per interest conversion period, by accumulating, at compound interest for the fraction m - l/2m of an interest conversion period, the present value of the same type of annuity with one payment per interest conversion period.

Description: In addition to death and maturity guarantees on the mutual funds they sell, some insurance companies make it possible for the investor to extend the guarantees for a fixed number of years. In this paper, we consider the case when that option is of the European type that is, the investor, at maturity, can either close out the contract or extend it for the stated, fixed term. When extended, the guarantee is on the value of the fund at the original maturity date. The fund is assumed to be fully invested in common stock.

Description: This paper deals with how the credibility levels change based on this lack knowledge. Group insuraace models are used, bill some of tile techniques could apply to any insurance risk.