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In this paper, we consider a special nonlinear expectation problem on the special parameter space and give a necessary and sufficient condition for the existence of the solution. Meanwhile, we generalize the necessary and sufficient condition to the two-dimensional moment problem. Moreover, we use the maximum entropy method to carry out a kind of concrete solution and analyze the convergence for the maximum entropy solution. Numerical experiments are presented to compute the maximum entropy density functions.

Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation