1 / 10

American Derivative Securities

American Derivative Securities. Presenter:Ting-Hsuan Long. 8.1 Introduction. 8.2 Stopping time. Discrete time Continuous time should be in F(t). Definition8.2.1. A stopping time is a r.v taking values in [0,∞] and satisfying (8.2.1). Remark8.2.2.

mora
Download Presentation

American Derivative Securities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. American Derivative Securities Presenter:Ting-Hsuan Long

  2. 8.1 Introduction

  3. 8.2 Stopping time • Discrete time • Continuous time should be in F(t)

  4. Definition8.2.1 • A stopping time is a r.v taking values in [0,∞] and satisfying (8.2.1)

  5. Remark8.2.2

  6. Example8.2.3(First passage time for a continuous process) • :adapted process with continuous paths • Show that is a stopping time. Let be given. We need to show thatis in F(t).

  7. Proof: Case1: depending on whether . In either case,

  8. Case2: step(1) Suppose In this interval, . is in the set A= We have shown that A

  9. step(2) If Let and X has a continuous path, we see that . It follows that . We have shown that Under these two step,

  10. step(3) Because there are only countably many rational numbers q in [0,t], they can be arranged in a sequence, and the union is really a union of a sequence of sets in F(t). We conclude that A

More Related