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...nancial models. However prospect theory and cumulative prospect theory have not been used in portfolio theory for infinite state spaces until the recent papers of Berkelaar et al [2] and Jin and Zhou =-=[13]-=-. Berkelaar et al [2] consider the EU contingent consumption demand problem for the convex-concave utility index introduced by Kahneman-Tverski [22] while Jin and Zhou [13] considers a general CPT con...

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... discounting [1, 14] and continuous-time mean–variance portfolio selection model [20, 2] provide two well-known examples of time-inconsistency. Probability distortion, as in behavioral finance models =-=[11]-=-, is yet another distinctive source of time-inconsistency. One way to get around the time-inconsistency issue is to consider only precommitted controls (i.e., the controls are optimal only when viewed...

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...and we remark further that, in the first paper, no probability distortions are considered, which considerably simplifies the problem). The only studies about the whole real line case are Jin and Zhou =-=[8]-=- and Rásonyi and Rodrigues [16]. Jin and Zhou [8] find explicit solutions in certain cases, but under hypotheses (see Assumption 4.1 therein) which are neither easily verifiable nor economically inter...

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...pirit from all the other works cited. Due to the mathematical difficulties, continuous-time studies focussed mainly on the case of complete markets where every contingent claim can be replicated; see =-=[6, 2, 19, 5, 10, 32, 28, 29]-=-. Market completeness is a rather unrealistic assumption hence it was desirable to treat incomplete models as well. In continuous-time, however, incompleteness presents considerable difficulties, and ...

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...hossoub (2009) [3] have carried out analytical treatment on singleperiod portfolio choice models and obtained closed-form solutions for a number of interesting cases. Importantly, Jin and Zhou (2008) =-=[15]-=- first analytically developed new approaches in driving the optimal solution by proposing a quantile formulation. I extend the Jin and Zhou (2008) [15] model by considering an optimization problem of ...

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...T. Alternative theories have been proposed to address the drawbacks of EUT, such as Prospect Theory by Kahneman and Tversky (1979), Rank-Dependent Utility by Quiggin (1982), and Cumulative Prospect Theory (CPT) by Tversky and Kahneman (1992). CPT can explain diminishing sensitivity, loss aversion, and different risk attitudes. Furthermore, unlike prospect theory, CPT does not violate the first-order stochastic dominance. The detailed characterizations of CPT are presented in Subsection 2.2. In this paper, we study optimal investment problems under the CPT framework including transaction cost. Jin and Zhou (2008) solve the problem in a continuous time model without transaction cost (Black-Scholes model) by splitting it into two Choquet optimization problems. The completeness of the market (the unique pricing kernel) plays an essential role in solving the problem in their paper, see also Carlier and Dana (2011). Optimal investment in a single-period discrete model under CPT, again without transaction cost, has been studied, e.g., by Bernard and Ghossoub (2010), He and Zhou (2011), Pirvu and Schulze (2012), and Carassus and Rasonyi (2015). Bernard and Ghossoub (2010) obtain an explicit optimal solution...