Should a central bank accommodate energy price shocks? Should the central bank use core inflation or headline inflation with the volatile energy component in its Taylor rule? To answer these questions, we build a dynamic stochastic general equilibrium model with energy use, durable goods, and nominal rigidities to study the effects of an energy price shock and its impact on the macroeconomy whe...

In this paper, we propose a recursive Taylor method for ray-casting algebraic surfaces. The performance of this approach is compared with four other candidate approaches to raycasting: using interval arithmetic on the power form, using interval arithmetic on centered forms, using affine arithmetic, and using modified affine arithmetic. Test results show that the recursive Taylor method compares...

This paper studies the applicability of the Taylor method for the sensibility analysis of ODEs and DAEs. Extended automatic differentiation rules are introduced for the calculus of partial derivatives of Taylor series. The numerical method is implemented using an efficient variablestep variable-order scheme. Finally, some numerical tests are presented showing the benefits of the formulation.

An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which are uniquely characterized by generalized Lyapunov equations. A numerical method for solving these equations is proposed. It is based on a generalization of ...

This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. Finally, the error analysis and some numerical examples are provided...

A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...

in this paper, we introduce an efficient method based on haar wavelet to approximate a solutionfor the two-dimensional linear stochastic fredholm integral equation. we also give an example to demonstrate the accuracy of the method.

In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The stochasticity of the gradient can be mitigated by the injection of Gaussian nois...

This paper examines methods to reduce systematic and random errors in simulations of interest rate models based on non-solvable, non-linear stochastic differential equations (SDEs). The paper illustrates how application of high-order Ito-Taylor discretization schemes in combination with appropriate variance reduction techniques can yield very significant improvements in speed and accuracy. Besi...

In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black-Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal proxy model. The final formulae are respectively first, second and third order approximations w.r.t. th...