Some properties of the optimal investment strategy in a behavioral portfolio choice model
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Some properties of the optimal investment strategy in a behavioral portfolio choice model Youcheng Lou1 Received: 26 October 2018 / Accepted: 16 August 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract The aim of this manuscript is to analyze the monotonicity and limit properties of the optimal investment strategy in a behavioral portfolio choice model under cumulative prospect theory over risk aversion coefficient, loss aversion coefficient, and the market opportunity. We show that the optimal investment strategy is nonincreasing of the loss aversion coefficient, and strictly increasing of the Sharpe ratio for normal distributions. The monotonicity properties over risk aversion coefficient depend on the position of the investor and the goodness of the actual and perceived market. The piecewiselinear utility is also discussed. An interesting finding is that when the excess return follows an elliptical distribution, the optimal investment strategy over small mean for piecewise-power and piecewise-linear utility exhibits different limit behavior. Keywords Cumulative prospect theory (CPT) · Behavioral portfolio choice (BPC) · Monotonicity properties
1 Introduction Cumulative prospect theory (CPT) has became a powerful tool to capture investors’ psychology in decision-making [7,17]. Several single-period behavioral portfolio choice (BPC) models under CPT have been studied in the literature [2,5,8,9,11]. He and Zhou [5] consider a quite general setting and derive the optimal investment strategy (OIS) for two special cases with a piecewise-linear-utility and zero-relative-wealth. He and Zhou [5] also show that the CPT preference value function is not concave on either the positive or the negative half space, and consequently, it is difficult to present a closed-form solution for BPC models in general.
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Youcheng Lou [email protected] MDIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55 Zhongguancun East Road, Beijing 100190, China
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Y. Lou
Because of the non-concavity of CPT preference value functions, most of the literature aims to analyze the properties of OISs or obtain semi-closed OISs. For instance, Bernard and Ghossoub [2] consider a no-shorting restriction and probability distortion, where the reference point corresponds to the terminal wealth when investing the entire initial wealth in the risk-free asset, and show that the OIS is a function of a generalized Omega measure of the distribution of the excess return on the risky asset over the risk-free rate. Pirvu and Schulze [11] investigate a model with multiple risky assets which follow a joint elliptical distribution, and obtain a semi-closed OIS by transferring the multi-dimensional optimization problem into a one-dimensional optimization problem. Minsuk and Pirvu [10] consider a model with multiple risky assets which follow a Skewed t distribution, and obtain a semi-closed OIS by reducing the multidimensional optimization problem into two one-dimensional optimization problems. Lou et al
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