American derivative securities
Download
1 / 10

American Derivative Securities - PowerPoint PPT Presentation


  • 102 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' American Derivative Securities' - mora


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
American derivative securities

American Derivative Securities

Presenter:Ting-Hsuan Long



8 2 stopping time
8.2 Stopping time

  • Discrete time

  • Continuous time

    should be in F(t)


Definition8 2 1
Definition8.2.1

  • A stopping time is a r.v taking values in [0,∞] and satisfying

    (8.2.1)



Example8 2 3 first passage time for a continuous process
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).


Proof
Proof:

Case1:

depending on whether .

In either case,


Case2:

step(1)

Suppose

In this interval, . is in the set

A=

We have shown that A


step(2)

If

Let and X has a continuous path, we see that . It follows that .

We have shown that

Under these two step,


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


ad