Remarks on t he Pricing of Contingent Claims under Const raint s A . B en so u ssa n University of Paris-Dauphine Place du M ar¶echal de Lat t re de Tassigny Paris Cedex 16, 75775, France (e-mail: Al ai n-Bensoussan@wanadoo.fr) Mar ch 27, 2003 1 Introduction In this paper we consider the results of I. Karatzas, S.E. Shreve [5] related t o t he probl em of cont ingent cl aims wit h const raint s, see also I . K arat zas, S.G. Kou [4]. We propose a di®erent approach, which is more analytic, and also more el ement ary and st raight forward. However, it is l imit ed t o t he case when the Dynamic Programming approach is possible Our approach has also t he advant age of working wi t hout any consumpt ion pr ocess, whi ch t urns out t o be somewhat art i¯ cial and sli ght ly confusing. 2 SETTING OF THE PROBLEM 2.1 A SSU M P T I ON S Let - ;A = Borel ¾¡ algebr a on - ; P; a probabili ty space, equipped wit h a ¯ l t rat ion and a n di mensional st andard- ized Wiener process for this ¯ ltration F s ;w(s): 1