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Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Linear filtering of systems with memory
| Title: | Linear filtering of systems with memory |
| Authors: | Inoue, Akihiko Browse this author | | Nakano, Yumiharu Browse this author | | Anh, Vo Browse this author |
| Keywords: | Filtering | | systems with memory | | stationary increment processes | | innovation processes | | Gaussian processes | | portfolio optimization |
| Issue Date: | 2004 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 657 |
| Start Page: | 1 |
| End Page: | 25 |
| Abstract: | We study the linear filtering problem for systems driven by continuous Gaussian processes V1 and V2 with memory described by two parameters. The processes Vj have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. It allows for straightforward parameter estimations. After giving the semimartingale representations of Vj by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69463 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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