Description: This paper presents a methodology of pricing the guaranteed minimum death benefit of a variable annuity in a market model with jumps. Recent developments in the stock market make variable annuities very attractive products from the insured point of view, but less attractive for insurers. The insured still has the possibility of investment benefits, while avoiding the risk of a stock market collapse. The insurer wants to minimize its risk and yet sell a competitive product. The financial market model consists of one riskless asset and one risky asset whose price jumps in proportions J at some random times T which correspond to the jump times of a Poisson process. The model describes incomplete markets and there is no perfect hedging. In the second part of the paper, we describe a possible method of risk analysis for binomial tree models.

Description: This is a letter from Jan M. Hoem to Arnold F. Shapiro about Exposed-to-risk considerations based on the Balducci assumption and other assumptions in the analysis of mortality.

Description: Investment Fallacies: The Best Model Doesn't Win

Description: This is the abstract of the article 'A Proposed Unified Valuation System'. This article will briefly describe some analytical examples of a stochastic modeling of risk use to illustrate the S-curve approach to valuation, but more importantly describe key additional area of research and theory, which need to be developed. The focus of this presentation is an invitation for additional research to support a new approach to statutory valuation of life and health risk that can result in better management and regulatory information.

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: 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: 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.