Description: This is a concluding and encompassing part of our research on the project entitled \Weighted Premium Calculation Principles and Risk Capital Allocations, which has been supported by the Actuarial Education and Research Fund AERF and the Society of Actuaries Committee on Knowledge Extension Research CKER. We explore the concept of weighted distributions and their role in various phenomena occurring in insurance and finance. In particular, we relate weighted distributions to actuarial and economic premium calculation principles, and also to the capital asset pricing model CAPM. Imitating the latter, we propose a weighted insurance pricing model WIPM. Although general in formulation, we show that the WIPM can successfully be evaluated in a variety of situations, which we illustrate with a number of examples.

Description: In a series papers by Willmot and Lin, both exponential and non-exponential bounds for the tail probability of various compound distributions have been derived. In Wilmot, it was suggested that non-exponential bounds for the ruin probability were difficult to obtain using martingale arguments. In this note, we show how to use martingale inequalities to obtain some upper bounds for the ruin probability.

Description: We propose asymptotically correct two-sided bounds for random sums where the number of summands has an arbitrary distribution which can be viewed as ruin probabilities or accumulated claim sizes in various risk processes. The bounds are fairly new and they reveal the real accuracy of some well-known and widely used asymptotic formulas. It turns out that this accuracy can be poor and the range where these formulas give appropriate approximations depends on the shape of the tail distribution of the summands. This dependence is examined in the research.

Description: Investment Fallacies: Mathematical modeling of social phenomena

Description: Investment Fallacies: On the Validity of Common Portfolio Return Assumptions

Description: Investment Fallacies: Gambler’s Fallacy: Probability of Reversion

Description: Since solvency assessment depends on a financial reporting framework, one needs risk metrics for use in financial reporting. The essay argues that conceptually, the cost of capital is the appropriate metric for reserves, while a probability level is the appropriate metric for capital. Then the essay advocates stress testing on specific scenarios as a better practical approach to ORSA.

Description: background history of the insurance industry and the role of actuaries within it, followed by the current environment and anticipated future environment.

Description: Panel discussion focused on the Effective Use of Capital. Topics included: 1. Definition of capital 2. Appropriate level of capital and surplus in a life insurance company 3. Alternatives for deploying capital 4. Returns a life company should demand on invested capital 5. How much a company should charge for lending its capital in reinsurance transactions

Description: The main objective of this study is to analyze and control a surplus dependent risk process, where larger surpluses allow for a wider underwriting policy. We focus here mostly on the diffusion approximation of the risk process. The results are derived in two papers Brownian motion in Risk Theory, submitted for publication, and Surplus dependent risk processes defined by stochastic differential equations, in preparation. We only include here a long summary of these papers.