Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that, for a utility function \(\) having reasonable asymptotic elasticity , the optimal investment process \(\) is a super-martingale under each equivalent martingale measure \(\), such that \(\), where V is the conjugate function of U. Similar results for the special case of the exponential utility re recently obtained by Delbaen, Grandits, Rheinlander, Samperi, Schizer, Stricker as ll as Kabanov, Stricker.
['Walter Schachermayer']
I am writing a research paper on a idea A Super-Martingale Property of the Optimal Portfolio Process
[{"from": "human", "value": "I am writing a research paper on a idea A Super-Martingale Property of the Optimal Portfolio Process"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that, for a utility function \\(\\) having reasonable asymptotic elasticity , the optimal investment process \\(\\) is a super-martingale under each equivalent martingale measure \\(\\), such that \\(\\), where V is the conjugate function of U. Similar results for the special case of the exponential utility re recently obtained by Delbaen, Grandits, Rheinlander, Samperi, Schizer, Stricker as ll as Kabanov, Stricker."}]