Investors' preferences are usually based on expected utility theory, but new theories like cumulative prospect theory (CPT) are challenging traditional models. This study explores CPT with an S-shaped utility function and distorted probability measures in incomplete diffusion market models. The researchers found that, even in these complex models, there exists an optimal investment strategy when certain conditions are met, such as non-negative returns and independence between economic factors and investment noise. This expands our understanding of how to make optimal investment decisions in real-world scenarios.