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: We consider Libor market model and calibration process. We estimate some interest rate derivatives such as Caps and Swaptions. We use Monte Carlo methods with appropriate dynamics under spot measure and forward measure. Imposing martingale discretization property, the same quantities are estimated again to see a contrast or discrepancy in light of confidence interval. Based on algorithms discussed in the paper, “Arbitrage-free discretizations of lognormal forward Libor and swap rate models” by Glasserman, P and Zhao, X 2000, the algorithms are implemented in excel VBA. Starting with current market data such as FRAs and Bond Prices, we describe steps involved to estimate the price of interest rate derivatives such as Caps and Swaptions, which would be beneficial to the practitioners in the industry.

Description: This is a presentation from 43rd Actuarial Research Conference ARC, Regina, August 14–16, 2008. This talk will present the moment generating function of the discounted compound Poisson aggregate sums when the deflated claims are PH distributed and moment generating function of the discounted compound renewal sums.

Description: This research was funded by the Natural Sciences and Engineering Research Council of Canada [NSERC] Discovery Grant 36860–06. Loss reserving is one of the most challenging tasks facing actuaries. Numerous approaches have been developed to give reasonable estimates. Generalized linear models [GLMs] are becoming quickly popular statistical analysis methods to estimate loss reserves. However, most of these models are aggregate reserving methods based on loss development triangles, without using information with regard to the actual claims processes. This paper establishes a more sophisticated structural reserving method incorporating more detailed information, such as the premium exposure emergence pattern, the loss emergence pattern and the loss development pattern, within the framework of GLMs.

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: This abstract describes a paper that presents preliminary observations with respect to probabilistic fuzzy systems.

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: This paper is Part 1 of a two-part submission. Part 2, “An Alternative Approach to Capital Allocation,” discusses using risk-replicating techniques that directly calculate the cost of capital. Such techniques can be used as a substitute for capital allocation. This paper expands upon current capital analysis by introducing a practical approach that considers the objectives of all stakeholders of an insurance company in setting appropriate capital targets.

Description: An overview of guaranteed lifetime withdrawal benefits (GLWB) on registered index-linkedannuity (RILA) products and a stochastic analysis of market risks.