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Superhedging under ratio constraint
Institution:1. Department of Mathematics, South China University of Technology, China.;2. Department of Mathematics and Risk Management Institute, National University of Singapore, Singapore.;3. Key Laboratory of Random Complex Structures and Data Science, Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, China.;1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;2. Department of Mathematics, University of New Orleans, New Orleans 70148, USA;3. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;1. Department of Economics, Indiana University, Bloomington, IN 47405, USA;2. European University in St. Petersburg, 3 Gagarinskaya Street, St. Petersburg, 191187, Russia;3. St. Petersburg Institute for Economics and Mathematics (Russian Academy of Sciences), 36-38 Serpukhovskaya Street, St. Petersburg, 190013, Russia;4. St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia;5. Department of Economics, Finance & Real Estate, Feliciano School of Business, Montclair State University, Montclair, NJ 07043, USA;1. Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6, Paris, France;2. Laboratoire de Mathématiques et Modélisation d’Évry (LaMME), Université d’Evry-Val d’Essonne, UMR CNRS 8071, 91025 Évry Cedex, France;3. Institut de Science Financière et d’Assurances (ISFA), Université Claude Bernard - Lyon 1, 50 Avenue Tony Garnier, 69007 Lyon, France;4. Beijing International Center for Mathematical Research (BICMR), Peking University, 100871 Beijing, China
Abstract:We consider superhedging of contingent claims under ratio constraint. It has been widely recognized that the minimum cost of superhedging a contingent claim with certain portfolio constraints is equal to the price of a claim with appropriately modified payoff but without constraints. In terms of the backward stochastic differential equation (BSDE) and the variational inequality equation approach, we revisit this result and provide two counterexamples.
Keywords:Superhedging  Ratio constraint  European option  Asian option
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