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: 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: Provides the actuary with a more satisfactory basis for annuity premiums and reserves. It presents a new mortality basis and offers a description of its construction. It also provides a historical review of past mortality tables for annuities. From the Society of Actuaries 50th Anniversary Monograph, M-AV99-1.

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.

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: Obsolescence of physical assets and processes is a major component of operational risk for some companies. A simulation experiment shows that managers, who consider the retirement and replacement of individual assets in isolation, have rational incentives, due to risk aversion and uncertainty, to defer the replacement of assets past a time that is optimal from the perspective of the shareholder who owns the entire portfolio of such assets. This results in measurable wealth destruction, —and a demonstrable opportunity to significantly enhance a company’s value. A practical decision model for the replacement timing of fixed, physical assets, which creates wealth by minimizing the long-term consumption of scarce resources, is provided.

Description: Empirical evidence of reported losses suggests that insurance firms are interconnected in a nontrivial way, making them prone to systemic risk. Systemic risk can be viewed as the result of a cascading process, as it unravels throughout a network structure. In response, this work presents a simple analytical model that can simulate this process. The model is subsequently tested upon an empirical dataset via the means of numerical simulations. This work makes three main contributions. First, it provides a novel methodology for quantitatively and objectively assessing the systemic role of individual firms within the insurance domain. Second, it exemplifies the inability of traditional, firm-based information in serving as proxies for mapping these systemic effects. Third, it provides a practical example where network-based information (e.g., Criticality IDX, Sensitivity IDX) can outperform firm-based information (e.g., admissible assets, excess c apital) resulting in increased efficiency in the decision-making process. These findings strengthen the need to account for the interconnected nature of the domain while showcasing some of the potential benefits that can be harvested by doing so.

Description: Empirical evidence of reported losses suggests that insurance firms are interconnected in a nontrivial way, making them prone to systemic risk. Systemic risk can be viewed as the result of a cascading process, as it unravels throughout a network structure. In response, this work presents a simple analytical model that can simulate this process. The model is subsequently tested upon an empirical dataset via the means of numerical simulations. This work makes three main contributions. First, it provides a novel methodology for quantitatively and objectively assessing the systemic role of individual firms within the insurance domain. Second, it exemplifies the inability of traditional, firm-based information in serving as proxies for mapping these systemic effects. Third, it provides a practical example where network-based information (e.g., Criticality IDX, Sensitivity IDX) can outperform firm-based information (e.g., admissible assets, excess c apital) resulting in increased efficiency in the decision-making process. These findings strengthen the need to account for the interconnected nature of the domain while showcasing some of the potential benefits that can be harvested by doing so.