scholarly journals Dynamic Money Doctors under Cumulative Prospect Theory

2019 ◽  
pp. 1-26
Author(s):  
Liurui Deng ◽  
Lan Yang ◽  
Bolin Ma
Keyword(s):  
Prospect Theory ◽  
Portfolio Selection ◽  
Value Function ◽  
Cumulative Prospect Theory ◽  
Risky Asset ◽  
Investment Strategies ◽  
Portfolio Choices ◽  
Portfolio Managers ◽  
Dynamic Portfolio ◽  
Mean Variance

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.

scholarly journals Research on the Multi-Period Optimal Fee of the Money Manager Under Cumulative Prospect Theory

2019 ◽  
Vol 1 (2) ◽  
pp. 29
Author(s):  
Liurui Deng ◽  
Lan Yang ◽  
Bolin Ma
Keyword(s):  
Prospect Theory ◽  
Optimal Strategy ◽  
Cumulative Prospect Theory ◽  
Investment Strategies ◽  
Risky Assets ◽  
Dynamic Framework ◽  
Portfolio Managers ◽  
Money Manager ◽  
Dynamic Portfolio ◽  
Mean Variance

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.

scholarly journals Multi-Period Investment Strategies under Cumulative Prospect Theory

2019 ◽  
Vol 12 (2) ◽  
pp. 83 ◽  
Author(s):  
Liurui Deng ◽  
Traian A. Pirvu
Keyword(s):  
Numerical Analysis ◽  
Prospect Theory ◽  
Portfolio Selection ◽  
Cumulative Prospect Theory ◽  
Risky Asset ◽  
Model Parameters ◽  
Investment Strategies ◽  
Portfolio Constraints ◽  
Risk Criterion ◽  
Optimal Portfolio Selection

In this article, inspired by Shi et al., we investigate the optimal portfolio selection with one risk-free asset and one risky asset in a multiple period setting under the cumulative prospect theory (CPT) risk criterion. Compared with their study, our novelty is that we consider a stochastic benchmark and portfolio constraints. By performing a numerical analysis, we test the sensitivity of the optimal CPT investment strategies to different model parameters.

Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market

2019 ◽  
Vol 53 (4) ◽  
pp. 1171-1186
Author(s):  
Reza Keykhaei
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Exit Time ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Homogeneous Markov Chain ◽  
Investment Strategies ◽  
Special Cases ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, we deal with multi-period mean-variance portfolio selection problems with an exogenous uncertain exit-time in a regime-switching market. The market is modelled by a non-homogeneous Markov chain in which the random returns of assets depend on the states of the market and investment time periods. Applying the Lagrange duality method, we derive explicit closed-form expressions for the optimal investment strategies and the efficient frontier. Also, we show that some known results in the literature can be obtained as special cases of our results. A numerical example is provided to illustrate the results.

scholarly journals Trapezoidal Intuitionistic Fuzzy Multiattribute Decision Making Method Based on Cumulative Prospect Theory and Dempster-Shafer Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xihua Li ◽  
Fuqiang Wang ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Value Function ◽  
Cumulative Prospect Theory ◽  
Intuitionistic Fuzzy Numbers ◽  
Attribute Weight ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Fuzzy Environment ◽  
Shafer Theory

With respect to decision making problems under uncertainty, a trapezoidal intuitionistic fuzzy multiattribute decision making method based on cumulative prospect theory and Dempster-Shafer theory is developed. The proposed method reflects behavioral characteristics of decision makers, information fuzziness under uncertainty, and uncertain attribute weight information. Firstly, distance measurement and comparison rule of trapezoidal intuitionistic fuzzy numbers are used to derive value function under trapezoidal intuitionistic fuzzy environment. Secondly, the value function and decision weight function are used to calculate prospect values of attributes for each alternative. Then considering uncertain attribute weight information, Dempster-Shafer theory is used to aggregate prospect values for each alternative, and overall prospect values are obtained and thus the alternatives are sorted consequently. Finally, an illustrative example shows the feasibility of the proposed method.

Humans, Econs and Portfolio Choice

2016 ◽  
Vol 07 (02) ◽  
pp. 1750001 ◽  
Author(s):  
Michael J. Best ◽  
Robert R. Grauer
Keyword(s):  
Prospect Theory ◽  
Portfolio Choice ◽  
Loss Aversion ◽  
Asset Allocation ◽  
Power Utility ◽  
Numerical Example ◽  
Portfolio Choices ◽  
Out Of Sample ◽  
Finance Theory ◽  
Mean Variance

We compare the portfolio choices of Humans — prospect theory investors — to the portfolio choices of Econs — power utility and mean-variance (MV) investors. In a numerical example, prospect theory portfolios are decidedly unreasonable. In an in-sample asset allocation setting, the prospect theory results are consistent with myopic loss aversion. However, the portfolios are extremely unstable. The power utility and MV results are consistent with traditional finance theory, where the portfolios are stable across decision horizons. In an out-of-sample asset allocation setting, the power utility and portfolios outperform the prospect theory portfolios. Nonetheless the prospect theory portfolios with loss aversion coefficients of 2.25 and 2 perform well.

scholarly journals Viscosity Solution of Mean-Variance Portfolio Selection of a Jump Markov Process with No-Shorting Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Moussa Kounta
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Portfolio Selection ◽  
Viscosity Solution ◽  
Value Function ◽  
Auxiliary Problem ◽  
Partial Differential ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
The Value Function

We consider the so-called mean-variance portfolio selection problem in continuous time under the constraint that the short-selling of stocks is prohibited where all the market coefficients are random processes. In this situation the Hamilton-Jacobi-Bellman (HJB) equation of the value function of the auxiliary problem becomes a coupled system of backward stochastic partial differential equation. In fact, the value functionVoften does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (classical) sense; however, in such casesVcan be interpreted as a viscosity solution. Here we show the unicity of the viscosity solution and we see that the optimal and the value functions are piecewise linear functions based on some Riccati differential equations. In particular we solve the open problem posed by Li and Zhou and Zhou and Yin.

An analytical approach for behavioral portfolio model with time discounting preference

2018 ◽  
Vol 52 (3) ◽  
pp. 691-712
Author(s):  
Guang Yang ◽  
Xinwang Liu ◽  
Jindong Qin ◽  
Ahmed Khan
Keyword(s):  
Portfolio Selection ◽  
Investment Strategy ◽  
Cumulative Prospect Theory ◽  
Investment Strategies ◽  
Short Term ◽  
Time Discounting ◽  
Present Bias ◽  
Proposed Model ◽  
Portfolio Selection Model

This paper presents a behavioral portfolio selection model with time discounting preference. Firstly, we discuss the portfolio selection problem and then modify this model based on cumulative prospect theory (CPT) as well as considering investors’ time discounting preference in psychology. Furthermore, an analytical solution with satisfying behavior is given for our proposed model, the results show that when investors’ goals are very ambitious, they put a high proportion of their wealth in long-term goals and adopt aggressive investment strategies with high leverage to reach short-term goals and the overall investment strategy also displays high leverage. Finally, numerical analysis is given and it is shown that investor who tends to future bias performs adequate confidence and patience whereas investor with present bias is apt to the immediate interests.

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