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: 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.

Description: In this paper, we study a survival regression model known as Cox's proportional Hazards model. We assume that the data available are already grouped and develop a minimum distance estimation procedure that is also applicable when the data are also left or right censored. Asymptotic properties of the estimators are established and the numerical implementation of the method based on an iterated reweighted least squares algorithm is discussed.

Description: This paper establishes the need for home equity conversion schemes for the elderly. It then provides a review of literature pertinent to reverse mortgages paying particular attention to the different types of reverse mortgages and their associated risks. In an attempt to better quantify the general appreciation risk faced by financial institutions issuing reverse mortgages, ARIMA techniques are employed to model Canadian house prices in both current and real dollar terms.

Description: In this note, we rearrange the statement and the proof of a theorem in Greville. The presentation appears to be more compact the materials, however, are not new.].

Description: American actuaries are increasingly involved in risk management. This paper presents an Overview of the role of the American actuary in risk management today, a book review of a remarkable new work by a philosopher of science, and a challenge to the reader.

Description: This article investigates the simplicity of the Balducci hypothesis, and compares the fractional-age death probability given by three widely used assumptions: uniform distribution of deaths, the Balducci hypothesis, and constant force of mortality [1, 2].

Description: In this paper we discuss some properties of the nth stop-loss order and their application in risk premium principles. We give a necessary condition and a sufficient condition for nth stop-loss orders. They are convenient tools to construct risk pairs with nth stop-loss orders. We show that exponential premium principles can diferentiate between losses more finely than the net premium principles under some conditions.

Description: The purpose of this paper is to survey some new results concerning the term structure of interest rates and discuss actuarial applications. The term structure of interest rates exhibits the relationship among the yields on default free debt instruments of different maturities. Although there is a considerable volume of literature dealing with the determinants of the term structure the analysis has until recently been presented for the most part in a deterministic i.e. non- stochastic framework. This constrasts with the treatment of capital assets where equilibrium prices have been obtained under the assumption that returns on these assets are random variables.