Computational Algorithms for Moments of Accumulated Markov and Semi-Markov Rewards

Power moments for accumulated rewards defined on Markov and semi-Markov chains are studied. A model with mixed time-space termination of reward accumulation is considered for inhomogeneous in time rewards and Markov chains. Characterization of power moments as minimal solutions of recurrence system of linear equations, sufficient conditions for finiteness of these moments and upper bounds for them, expressed in terms of so-called test functions, are given. Backward recurrence algorithms for funding of power moments of accumulated rewards and various time-space truncation approximations reducing dimension of the corresponding recurrence relations are described.     

Analytical and numerical studies on the second-order asymptotic expansion method for European option pricing under two-factor stochastic volatilities

The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013, Chiarella and Ziveyi considered Christoffersen’s ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast (for example daily) and slow (for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first- and second-order asymptotic expansion formulas.     

Risk Analysis of PCB Exposure via the Soil–Food Crop Pathway, and Alternatives for Remediation at Serpukhov, Russian Federation

A risk assessment was conducted to determine the likelihood of certain health risks resulting from exposure to soils and food crops contaminated with polychlorinated biphenyl (PCBs). PCBs have contaminated soils, river sediments, and air in the past as a result of industrial activities at a capacitor plant located in the City of Serpukhov, Russian Federation. This risk assessment and suggestions for remediation are designed to aid in decision-making efforts by a joint Russian–American research team developing a community, national, and international response to industrial contamination. Bobovnikova et al. ( The Science of the Total Environment 139/140 , 357–364, [1993]) have reported that PCBs are elevated in soils and sediments, breast milk, and locally grown foods in the Serpukhov area. Data from these and other investigators have been used in this risk assessment to calculate a potential cancer risk resulting from exposure to PCBs. Our assessment indicates that members of the local population may be at increased risk of cancer, and possibly other adverse health effects, as a result of PCB contamination of their environment. Because previously unassessed environmental contamination is a common problem in the former Soviet Republics, as well as many other areas of the world, we believe this type of evaluation, using known methods, can serve as a model for assessment efforts in other parts of the globe and result in remediative efforts in regions constrained by faltering economies.