Economy – Quantitative Finance – Pricing of Securities
Scientific paper
2008-04-16
Annals of Probability 2008, Vol. 36, No. 2, 647-697
Economy
Quantitative Finance
Pricing of Securities
Published in at http://dx.doi.org/10.1214/009117907000000222 the Annals of Probability (http://www.imstat.org/aop/) by the Ins
Scientific paper
10.1214/009117907000000222
We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows, in particular, to solve the American optimal stopping problem without having to compute the option price. Some illustrative examples based on one-dimensional diffusion processes are then provided. Another interesting application concerns the portfolio insurance. Hence, based on the ``Max-Plus martingale,'' we solve in the paper an optimization problem whose aim is to find the best martingale dominating a given floor process (on every intermediate date), w.r.t. the convex order on terminal values.
Karoui Nicole El
Meziou Asma
No associations
LandOfFree
Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Max-Plus decomposition of supermartingales and convex order. Application to American options and portfolio insurance will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-607148