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We characterize the price of a European option on several assets for a very risk-averse seller, in a market with small transaction costs as a solution of a nonlinear diffusion equation. This problem turns out to be one of asymptotic analysis of parabolic PDE, and the interesting feature is the role of a nonlinear PDE eigenvalue problem. In particular, we generalize previous work of Guy Barles and H. Mete Soner who studied this problem for a European option on a single asset.doi:10.1080/03605302.2014.929145 fatcat:xpnj5ept6vdubfmbxcjzh5tjbq