大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

On singular control for Lévy processes

Kazutoshi Yamazaki (Kansai University)

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4. On singular control for Lévy processes

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第111回

On singular control for Lévy processes

Kazutoshi Yamazaki (Kansai University)

We revisit the classical singular control problem of minimizing running and controlling costs. The problem arises in inventory control, as well as in healthcare management and mathematical finance. Existing studies have shown the optimality of a barrier strategy when driven by the Brownian motion or Lévy processes with one-side jumps. Under the assumption that the running cost function is convex, we show the optimality of a barrier strategy for a general class of Levy processes. Numerical results are also given. (Joint work with Kei Noba, Osaka University)