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In this work we present a result on the non-existence of monotone, consistent linear discrete approximation of order higher than 2. This is an essential ingredient, if we want to solve numerically nonlinear and particularly Hamilton-Jacobi-Bellman (HJB) equations.

Force-gradient decomposition methods are used to improve the energy preservation of symplectic schemes applied to Hamiltonian systems. If the potential is composed of different parts with strongly varying dynamics, this multirate potential can be exploited by coupling force-gradient decomposition methods with splitting techniques for multi-time scale… (More)

The Quanto option is a cash-settled, cross-currency derivative in which the underlying asset has a payoff in one country, but the payoff is converted to another currency in which the option is settled. Thus, the correlation between the underlying asset and currency exchange rate plays an important role on pricing such options. Market observations give clear… (More)

The Cox-Ingersoll-Ross model (CIR model) [2] has been a benchmark in finance for many years because of its analytical and structural tractability. The wide applications and extensions of the CIR model requires to evaluate the cumulative distribution function (CDF) of the integrated CIR process in financial modelling. As in many situations the characteristic… (More)

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