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This paper proposes a novel numerical method for solving the problem of
decision making under cumulative prospect theory (CPT), where the goal is to
maximize utility subject to practical constraints, assuming only finite
realizations of the associated distribution are available. Existing methods for
CPT optimization rely on particular assumptions that may not hold in practice.
To overcome this limitation, we present the first numerical method with a
theoretical guarantee for solving CPT optimization using an alternating
direction method of multipliers (ADMM). One of its subproblems involves
optimization with the CPT utility subject to a chain constraint, which presents
a significant challenge. To address this, we develop two methods for solving
this subproblem. The first method uses dynamic programming, while the second
method is a modified version of the pooling-adjacent-violators algorithm that
incorporates the CPT utility function. Moreover, we prove the theoretical
convergence of our proposed ADMM method and the two subproblem-solving methods.
Finally, we conduct numerical experiments to validate our proposed approach and
demonstrate how CPT's parameters influence investor behavior using real-world
data.
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