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 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 Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion

2021 ◽  
Author(s):  
Bohan Li ◽  
Junyi Guo
Keyword(s):  
Optimal Strategy ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Capital Asset Pricing ◽  
Investment Strategies ◽  
Asset Pricing Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Zero Sum ◽  
Mean Variance

This paper considers the optimal investment-reinsurance problem under the monotone mean-variance preference. The monotone mean-variance preference is a monotone version of the classical mean-variance preference. First of all, we reformulate the original problem as a zero-sum stochastic differential game. Secondly, the optimal strategy and the optimal value function for the monotone mean-variance problem are derived by the approach of dynamic programming and the Hamilton-Jacobi-Bellman-Isaacs equation. Thirdly, the efficient frontier is obtained and it is proved that the optimal strategy is an efficient strategy. Finally, the continuous-time monotone capital asset pricing model is derived.

CONTINUOUS-TIME MEAN–VARIANCE OPTIMIZATION FOR DEFINED CONTRIBUTION PENSION FUNDS WITH REGIME-SWITCHING

2019 ◽  
Vol 22 (06) ◽  
pp. 1950029
Author(s):  
ZHIPING CHEN ◽  
LIYUAN WANG ◽  
PING CHEN ◽  
HAIXIANG YAO
Keyword(s):  
Brownian Motion ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Regime Switching ◽  
Efficient Frontier ◽  
Defined Contribution ◽  
Risky Assets ◽  
Mean Variance Portfolio ◽  
Mean Variance

Using mean–variance (MV) criterion, this paper investigates a continuous-time defined contribution (DC) pension fund investment problem. The framework is constructed under a Markovian regime-switching market consisting of one bank account and multiple risky assets. The prices of the risky assets are governed by geometric Brownian motion while the accumulative contribution evolves according to a Brownian motion with drift and their correlation is considered. The market state is modeled by a Markovian chain and the random regime-switching is assumed to be independent of the underlying Brownian motions. The incorporation of the stochastic accumulative contribution and the correlations between the contribution and the prices of risky assets makes our problem harder to tackle. Luckily, based on appropriate Riccati-type equations and using the techniques of Lagrange multiplier and stochastic linear quadratic control, we derive the explicit expressions of the optimal strategy and efficient frontier. Further, two special cases with no contribution and no regime-switching, respectively, are discussed and the corresponding results are consistent with those results of Zhou & Yin [(2003) Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model, SIAM Journal on Control and Optimization 42 (4), 1466–1482] and Zhou & Li [(2000) Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization 42 (1), 19–33]. Finally, some numerical analyses based on real data from the American market are provided to illustrate the property of the optimal strategy and the effects of model parameters on the efficient frontier, which sheds light on our theoretical results.

scholarly journals A Dynamic Mean-Variance Analysis for Log Returns

2020 ◽  
Author(s):  
Min Dai ◽  
Hanqing Jin ◽  
Steven Kou ◽  
Yuhong Xu
Keyword(s):  
Portfolio Choice ◽  
Choice Model ◽  
Risky Assets ◽  
Complete Market ◽  
Dynamic Portfolio ◽  
Short Sell ◽  
Dynamic Portfolio Choice ◽  
Risk Free Rate ◽  
Mean Variance

We propose a dynamic portfolio choice model with the mean-variance criterion for log returns. The model yields time-consistent portfolio policies and is analytically tractable even under some incomplete market settings. The portfolio policies conform with conventional investment wisdom (e.g., richer people should invest more absolute amounts of money in risky assets; the longer the investment time horizon, the more proportional amount of money should be invested in risky assets; and for long-term investment, people should not short-sell major stock indices whose returns are higher than the risk-free rate), and the model provides a direct link with the constant relative risk aversion utility maximization in a complete market. This paper was accepted by Kay Giesecke, finance.

OPTIMAL CONSTANT-REBALANCED PORTFOLIO INVESTMENT STRATEGIES FOR DYNAMIC PORTFOLIO SELECTION

2006 ◽  
Vol 09 (06) ◽  
pp. 951-966 ◽  
Author(s):  
ZHONG-FEI LI ◽  
KAI W. NG ◽  
KEN SENG TAN ◽  
HAILIANG YANG
Keyword(s):  
Risk Measure ◽  
Efficient Frontier ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Variance Model ◽  
Optimal Constant ◽  
Black Scholes ◽  
Dynamic Portfolio ◽  
Portfolio Optimization Problem ◽  
Mean Variance

In this paper we propose a variant of the continuous-time Markowitz mean-variance model by incorporating the Earnings-at-Risk measure in the portfolio optimization problem. Under the Black-Scholes framework, we obtain closed-form expressions for the optimal constant-rebalanced portfolio (CRP) investment strategy. We also derive explicitly the corresponding mean-EaR efficient portfolio frontier, which is a generalization of the Markowitz mean-variance efficient frontier.

scholarly journals Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Zhongbao Zhou ◽  
Xianghui Liu ◽  
Helu Xiao ◽  
TianTian Ren ◽  
Wenbin Liu
Keyword(s):  
Empirical Studies ◽  
Lagrange Function ◽  
Investment Strategy ◽  
Open Loop ◽  
Investment Strategies ◽  
Variance Model ◽  
Risky Assets ◽  
Consistent Solution ◽  
Mean Variance Portfolio ◽  
Mean Variance

The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.

scholarly journals Multi-period Investment Strategies with Transaction Costs Under Cumulative Prospect Theory

2019 ◽  
Vol 5 (2) ◽  
pp. 53
Author(s):  
Liurui Deng ◽  
Lan Yang ◽  
Bolin Ma
Keyword(s):  
Transaction Costs ◽  
Prospect Theory ◽  
Optimization Problem ◽  
Optimal Investment ◽  
Original Data ◽  
Cumulative Prospect Theory ◽  
Optimal Portfolio ◽  
Investment Strategies ◽  
Optimal Portfolios ◽  
The Impact

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.

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