This paper focuses on optimal investment strategies under cumulative prospect theory (CPT). Considering transaction costs, we investigate CPT investors multi-period optimal portfolios. Our main contributions relative to previous work are expanding a single-period optimization problem to a multi-period optimization problem and investigating the impact of transaction costs on optimal portfolio selections. In a numerical analysis that applied original data on four stocks from the NASDAQ, we examine the effects of different risks on the optimal portfolio. Moreover, in contrast with the results without transaction costs, we come to conclusion that the optimal strategy with transaction costs is less sensitive to risk.

We investigate the interaction between investors and portfolio managers under cumulative prospect theory. We model trust in the manager and the relative anxiety about investing in a risky asset in an original way. Moreover, we study how trust and anxiety affect the manager’s fee and the portfolios of cumulative prospect theory investors. In contrast to previous work using the classical mean-variance preferences, there are two main novelties in our contribution. First, our research relies on cumulative prospect theory (CPT) rather than the classical mean-variance framework. Second, we focus on a dynamic portfolio selection. In other words, we formulate the optimal problem under multi-period setting. Besides, we attain an optimal portfolio choices in multi-period relying on the sub-game perfect investment strategies. Moreover, our research differs from traditional CPT work through an improved value function that accurately characterizes the reduction in anxiety suffered by the CPT investors from bearing risk when assisted by the portfolio managers’ help relative to when they lack such assistance.

A portfolio manager can obtain profits from charging management fees to individual investors for helping them to invest. Moreover, as an insider, the portfolio manager can obtain proportional brokerage charges on the return on investment by investing the individual investors’ money that he manages. How does the manager balance money management and investment to maximize his total profits? This is the problem that we study in this article. We model the relationship between money management fees and the amount invested. In addition, we investigate how to determine money management fees and the amount of investment needed to maximize the manager’s total profits, including from management fees and brokerage charges.

We are interested in investors’ interaction with portfolio managers and investigate the manager’s optimal strategy under cumulative prospect theory. We create model to characterize the relative anxiety about investing in risk assets and trust in the manager. Besides, we research how anxiety and trust affect the manager’s fee and the investors’ portfolios under cumulative prospect theory. Compared with previous work, our main novelty is that we focus on a dynamic portfolio selection. In other words, we formulate the optimal problem under multi-period setting. Besides, relying on the sub-game perfect investment strategies, we attain an optimal fee in multi-period. Another contribution is to discuss multiple risky assets. We use elliptic distribution to reduce a high-dimensional optimal problem to a one-dimensional optimal one. We obtain the CPT-investors’ portfolio for multiple risky assets under a dynamic framework. Based on this result, we study the manager’s optimal fee. It is valuable to say that we explore the optimal strategy for the manager under cumulative prospect theory but not the classical mean-variance preferences.