... Chapter 7 Jensen’s Inequality 7.1 Jensen’s Inequality for Conditional ExpectationsLemma 1.23 If' : IR!IRis convex ... 'IE Yk+1jFk= 'Yk:7.2 Optimal Exercise of an American CallThis follows from Jensen’s inequality. Corollary 2.25 Given a convex functiong :0;1!IRwhereg 0 = 0. For instance,g ... 1we have (see Fig. 7.2):g x = g x +1,:0 g x+1, :g 0= g x:CHAPTER 7. Jensen’s Inequality 93( x, g(x))λλ( x, g( x))λλ(x,g(x))xFigure 7.2: Proof of Cor. 2.25Therefore,g11+rSk+111+rgSk+1andfIEh1...