{'fraction_non_alphanumeric': 0.022326674500587545, 'fraction_numerical': 0.01410105757931845, 'mean_word_length': 5.264705882352941, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Consumption and Investment Optimization Under Constraints

We analyze a problem of maximization of expected terminal wealth and consumption under constraints in a general financial framework, which includes models with constrained portfolios, labor income and large investor models. By introducing the new finite probability space, as well as a new utility function, the considered problem is converted to the one studied by Pham and Mnif (2002) [48]. By using general optional decomposition under constraints, we can develop a dual formulation under minimal assumption modeled as in Pham and Mnif (2002) [48]. We then are able to prove an existence and uniqueness of an optimal solution to primal problem. Under the assumption that there exists a solution to the corresponding dual problem, an optimal consumption plan can be found by convex duality.