In this paper, we outline an impulse stochastic control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB) assuming the policyholder is allowed to withdraw funds continuously. We develop a numerical scheme for solving the Hamilton-Jacobi-Bellman (HJB) variational inequality corresponding to the impulse control problem. We prove the convergence of our scheme to the viscosity solution of the continuous withdrawal problem, provided a strong comparison result holds. The scheme can be easily generalized to price discrete withdrawal contracts. Numerical experiments are conducted, which show a region where the optimal control appears to be non-unique.

The valuation of a gas storage facility is characterized as a stochastic control problem, resulting in a Hamilton-Jacobi-Bellman (HJB) equation. In this paper, we present a semi-Lagrangian method for solving the HJB equation for a typical gas storage valuation problem. The method is able to handle a wide class of spot price models that exhibit mean-reverting, seasonality dynamics and price jumps. We develop fully implicit and Crank-Nicolson timestepping schemes based on a semi-Lagrangian approach and prove the convergence of fully implicit timestepping to the viscosity solution of the HJB equation. We show that fully implicit timestepping is equivalent to a discrete control strategy, which allows for a convenient interpretation of the optimal controls. The semi-Lagrangian approach avoids the nonlinear iterations required by an implicit finite difference method without requiring additional cost. Numerical experiments are presented for several variants of the basic scheme.

Algorithms for solving linear systems of equations over the integers are designed and implemented. The implementations are based on the highly optimized and portable ATLAS/BLAS library for numerical linear algebra and the GNU Multiple Precision library (GMP) for large integer arithmetic.

In this paper, we propose a one-factor regime-switching model for the risk adjusted natural gas spot price and study the implications of the model on the valuation and optimal operation of natural gas storage facilities. We calibrate the model parameters to both market futures and options on futures. Calibration results indicate that the regime-switching model is a better fit to market data compared to a one-factor mean-reverting model similar to those used by other authors to value gas storage. We extend a semi-Lagrangian timestepping scheme from Chen and Forsyth (2007) to solve the gas storage pricing problem, essentially a stochastic control problem, and conduct a convergence analysis of the scheme. Numerical results also indicate that the regime-switching model can generate operational strategies for gas storage facilities that reflect the existence of multiple regimes in the market as well as the regime shifts due to various exogenous events.

ABSTRACT

The radiation-induced graft polymerisation of hydroxyethyl methacrylate on silk fabric has been studied using an electron beam irradiation technique. Two irradiation processes, pre-irradiation and coirradiation, were compared, and some factors affecting the degree of grafting were investigated. The physical and mechanical properties such as whiteness, breaking strength and resilience of the radiation-grafted silk fabrics were examined. The hydroxyethyl methacrylate grafting of silk with electron beam irradiation increases silk weight and improves the crease resistance of silk. Electron spin resonance technique shows the formation of free radical species on the electron beam irradiated silk and the rapid decay of radicals in water.

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