Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose and solve a general entrepreneurial/managerial decision-making problem. Instead of employing concave objective functions,  use a broad class of nonconcave objective functions.  approach the problem by a martingale method.  show that the optimization problem with a nonconcave objective function has the same solution as the optimization problem when the objective function is replaced by its concave hull, and thus the problems are equivalent to each other. The value function is shown to be strictly concave and to satisfy the Hamilton-Jacobi-Bellman equation of dynamic programming.  also show that the final alth cannot take values in the region where the objective function is not concave: the entrepreneur would like to avoid her or his alth ending up in the nonconcave region. Because of this, the entrepreneur’s risk taking explodes as time nears maturity if her his alth is equal to the right end point of the nonconcave region.
['Alain Bensoussan', 'Abel Cadenillas', 'Hyeng Keun Koo']
I am writing a research paper on a idea Entrepreneurial Decisions on Effort and Project with a Nonconcave Objective Function
[{"from": "human", "value": "I am writing a research paper on a idea Entrepreneurial Decisions on Effort and Project with a Nonconcave Objective Function"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose and solve a general entrepreneurial/managerial decision-making problem. Instead of employing concave objective functions,  use a broad class of nonconcave objective functions.  approach the problem by a martingale method.  show that the optimization problem with a nonconcave objective function has the same solution as the optimization problem when the objective function is replaced by its concave hull, and thus the problems are equivalent to each other. The value function is shown to be strictly concave and to satisfy the Hamilton-Jacobi-Bellman equation of dynamic programming.  also show that the final alth cannot take values in the region where the objective function is not concave: the entrepreneur would like to avoid her or his alth ending up in the nonconcave region. Because of this, the entrepreneur\u2019s risk taking explodes as time nears maturity if her his alth is equal to the right end point of the nonconcave region."}]