Description: Investment Fallacies: The Myth of Time Diversification

Description: Investment Fallacies: Future Equity Returns

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: Recurrence relations arise naturally in life contingencies for 2 reasons - the aggregate law of mortality, which relates the distribution of the future life times of 2 insureds, if one of them and the other is that most life insurance products can be constructed as a portfolio of 2 basic product types. We use the above simple idea and the extra freedom provided by the fractional age distribution to reveal a structure behind some common recursions. The structure has obvious pedagogical value. More interestingly, a software based on it has been implemented which facilitates actuarial computing.

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 examines claim transaction data as experienced in the Canadian pet insurance industry. The current practice is to use an exposure unit approach to estimate the pure premium cost. This approach is applied in this paper in order to reveal certain cost patterns in accident, illness and death benefit costs.

Description: Investment Fallacies: Simulation of Long-Term Stock Returns: Fat-Tails and Mean Reversion

Description: This article provides an overview of the financial results of managed care plans over time using a collection of the NAIC financial statements.

Description: The paper o ers a simple framework for ranking the common reinsurance struc- tures in practice with the theory of stochastic orders. The basic idea is to slice the space of reinsurance structures into groups by expected loss cost to facilitate the comparisons within the group and between groups. Given the standard risk aversion assumption in economics, a spectrum of reinsurance structures with the same expected loss cost can be compared analytically with one another and sequenced based on their risk coverages under the convex order. The paper then expands the dimension of the comparison to groups of reinsurance structures with di erent expected loss costs, which can be ranked under the increasing convex order and the usual stochastic order. As such, the paper maps out the ordering for the entire space of reinsurance structures and presents it in a ma- trix format for quick reference. The implication of this stochastic ordering to reinsurance pricing is also investigated.

Description: This paper presents a random selection method with the Monte Carlo simulation technique in the estimation of loss reserves. The future loss development factors are randomly selected from a weighted empirical distribution of observed loss development factors. This nonparametric approach provides an estimate of the distribution of total loss reserve.