Description: Presentation from the 41st Actuarial Research Conference held in August, 2006 in Montreal. This presentation extends the traditional Sparre Anderson model of ruin theory, using an Erlang distribution for inter-claim times and geometric Brownial motion for asset returns.

Description: Continuation of article from previous issue. This article illustrates the practical and financial implications of applying nested stochastic techniques to a sample product.

Description: This article is based on an excerpt from a Milliman Research Report on universal life insurance with secondary guarantees, ULSG. It discusses stochastic profit analysis and the impact of investment volatility of two common variants of ULSGs - level specified premium and single-fund shadow account designs.

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 purpose of this discussion is to introduce a few additional points and discuss how different assumptions will alter the results in some cases.

Description: Presentation discussing modeling of daily and hourly rainfall, both occurrence and amount. These distributions would be needed to price derivative or insurance contracts involving rainfall amounts.

Description: This presentation estimates several models of interest rates, including seven without and four with regime shifts.

Description: This presentation considers the pricing of European derivatives in a Black-Scholes model with stochastic volatility. The presentation shows how Parseval’s theorem may be used to express those prices as Fourier integrals. This is a significant improvement over Monte Carlo simulation in many cases. The main ingredient in this presentation's method is the Laplace transform of the ordinary [constant volatility] price of a put or call in the Black-Scholes model, where the transform is taken with respect to maturity [T]. The presentation derives these formulas and then applies them to the case where volatility is modelled as a Markov chain in continuous time, the so-called 'Markov regime switching model'. This model has been used previously in stochastic volatility modelling, but mostly with only N=2 states. The presentation shows how to use N=3 states without difficulty, and how larger number of states can be handled. Numerical illustrations are given, including the volatility smile in a three-state model.

Description: Modeling experience sharing by David Yu who leads the retirement product and asset model development team within Prudential Financial

Description: As stochastic modeling has evolved, it has divided down two paths—real-world and risk-neutral. This article discusses this division and shows how these paths may be re-united through the use of deflators.