Linear filtering of systems with memory and application to finance

A.Inoue; Y.Nakano; V.Anh

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Linear filtering of systems with memory and application to finance

机译：具有内存的系统的线性过滤及其在金融中的应用

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We study the linear filtering problem for systems driven bycontinuous Gaussian processesV(1)andV(2)with memorydescribed by two parameters. The processesV(j)have the virtue that they possess stationary increments and simplesemimartingale representations simultaneously. They allow forstraightforward parameter estimations. After giving thesemimartingale representations ofV(j)by innovation theory,we derive Kalman-Bucy-type filtering equations for the systems. Weapply the result to the optimal portfolio problem for an investorwith partial observations. We illustrate the tractability of thefiltering algorithm by numerical implementations.

机译：我们研究由连续高斯过程V（1）和V（2）驱动的系统的线性滤波问题，该过程由两个参数描述。进程V（j）的优点是它们同时具有固定增量和简单的半mart表示。它们允许直接进行参数估计。在通过创新理论给出了这些V（j）的小表示之后，我们推导了系统的卡尔曼-布西型滤波方程。通过部分观察，我们将结果应用于最优投资组合问题。我们通过数值实现来说明滤波算法的可处理性。

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《International journal of stochastic analysis》 |2006年第3期|共26页
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A.Inoue; Y.Nakano; V.Anh;
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Linear filtering of systems with memory and application to finance

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