Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study the problem of pricing American contingent claims in an incomplete market where the stock price process is supposed to be driven by both a Wiener process and a Poisson random measure and the portfolios are constrained.  formulate this problem as to find the minimal solution of a backward stochastic differential equation (BSDE) with constraints.  use the penalization method to construct a sequence of BSDEs with respect to Wiener process and Poisson random measure, and  show that the solutions of these equations converge to the minimal solution  are interested in. Finally, in the Markovian case,  characterize the minimal hedging price as the minimal viscosity supersolution of an integral-partial differential inequality with constraints.
['Rainer Buckdahn', 'Ying Hu']
I am writing a research paper on a idea Pricing of American Contingent Claims with Jump Stock Price and Constrained Portfolios
[{"from": "human", "value": "I am writing a research paper on a idea Pricing of American Contingent Claims with Jump Stock Price and Constrained Portfolios"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study the problem of pricing American contingent claims in an incomplete market where the stock price process is supposed to be driven by both a Wiener process and a Poisson random measure and the portfolios are constrained.  formulate this problem as to find the minimal solution of a backward stochastic differential equation (BSDE) with constraints.  use the penalization method to construct a sequence of BSDEs with respect to Wiener process and Poisson random measure, and  show that the solutions of these equations converge to the minimal solution  are interested in. Finally, in the Markovian case,  characterize the minimal hedging price as the minimal viscosity supersolution of an integral-partial differential inequality with constraints."}]