Description: The purpose of this paper is to provide a method for calculating special contingency reserves for investment losses. The method is derived by first building a stochastic investment model and then utilizing its probabilistic structure. From Transactions of Society of Actuaries 1980, Vol. 32.

Description: After reading the Panjer-Bellhouse paper in the Proceedings of the Ball State University Conference, I wondered whether their technique could be used when a realistic investment process was assumed. I believe that such an extension is necessary if the theory is to have any practical application I have had little success in trying to do this. I have decided to present some thoughts and to invite others with different perspectives to bring them to fruition.

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: From a session at a meeting of the Society of Actuaries held in San Diego, CA, June 22-23, 2000 A discussion of how stochastic modeling techniques can be used to efficiently and effectively consider a wide variety of scenarios and outcomes and how these tools can be used to optimize portfolio performance?

Description: This session at the SOA 2001 Toronto Spring Meeting offers an overview of stochastic pricing including stochastic variables, equity market models, interest rate models and policyholder behavior. An example is given using a variable annuity product.

Description: This is authors' Fellowship Credit Research Paper. This paper will develop a model for cash flow testing traditional participating insurance that utilizes pricing tools and assumptions to project reserve liabilities. The model makes use of finance and accounting tools to monitor the reasonableness of ending and intermediate surplus results that emerge under the various interest rate scenarios imposed.

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: 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: Without relying on formulas, this paper presents the important concepts underlying the theory of arbitrage-free pricing of interest-rate-contingent cash flows: absence of opportunities for riskless arbitrage, completeness of markets, relative prices that do not depend on individual investors' subjective views or risk preferences, and expected-value pricing in the risk-neutral world. Using these concepts, the paper then describes the steps required to build continuous stochastic models of interest rates, including models that are either partially or fully arbitrage free.