2020/06/16 by Martin Larsson, Larsson, Martin, Marvin S. Mueller +3
Decision Sciences · Economics, Econometrics and Finance · #49L20 #91A15 #91G20 #93E20 #Auction Theory and Applications #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2006.09493
openalex publication_date 2020/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2002, Benjamin Jourdain and Claude Martini discovered that for a class of payoff functions, the pricing problem for American options can be reduced to pricing of European options for an appropriately associated payoff, all within a Black-Scholes framework. This discovery has been investigated in great detail by Sören Christensen, Jan Kallsen and Matthias Lenga in a recent work in 2020. In the present work we prove that this phenomenon can be observed in a wider context, and even holds true in a setup of non-linear stochastic processes. We analyse this problem from both probabilistic and analytic viewpoints. In the classical situation, Jourdain and Martini used this method to approximate prices of American put options. The broader applicability now potentially covers non-linear frameworks such as model uncertainty and controller-and-stopper-games.