Advances in Mathematical Economics Volume 18 by Shigeo Kusuoka & Toru Maruyama

Author:Shigeo Kusuoka & Toru Maruyama
Language: eng
Format: epub
Publisher: Springer Japan, Tokyo

for t ∈ (0,T], s ∈ (0,t), and any bounded measurable function f defined in E.

6 Application to Bermuda Type Problem

Let us think of the situation in Sect. 4. Then we have the following.

Theorem 24.

Let 0 = T 0 < T 1 < … < T n < T, δ ∈ (0,1∕2), and for some Then there are C > 0, and measurable functions m = 1,…,n − 1, i = 1,2, such that

and

for any m = 1,…,n − 1.

Proof.

Note that for

So we see that

Similarly we have

Let us take a k , k = 0, 1, …, n such that 1∕2 > a 0 > a 1 > … > a n  > 1∕2 −δ. Also, let

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