This paper concerns the design of a Fourier based pseudospectral numerical method for the model of European option pricing with transaction costs under exponential utility derived by Davis, Panas and Zariphopoulou in Davis et al. (1993). Computing the option price involves solving two stochastic optimal control problems. With an exponential utility function, the dimension of the problem can be reduced, but one has to deal with high absolute values in the objective function. We propose two changes of variables that reduce the impact of the exponential growth and a Fourier pseudospectral method to solve the resulting non linear equation. Numerical analysis of the stability, consistency, convergence and localization error of the method are included. Numerical experiments support the theoretical results and the effect of incorporating transaction costs is also studied.

本文涉及Davis等人的Davis，Panas和Zariphopoulou得出的指数效用下具有交易成本的欧式期权定价模型的基于傅里叶伪谱数值方法的设计。（1993）。计算期权价格涉及解决两个随机的最优控制问题。使用指数效用函数，可以减小问题的范围，但是必须处理目标函数中的高绝对值。我们提出了两种减小指数增长影响的变量更改，以及一种傅里叶拟谱方法来解决由此产生的非线性方程。对该方法的稳定性，一致性，收敛性和定位误差进行了数值分析。