scholarly journals Multi-time state mean-variance model in continuous time

2021 ◽  
Vol 27 ◽  
pp. 92
Author(s):  
Shuzhen Yang
Keyword(s):  
Boundary Conditions ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Investment Portfolio ◽  
Variance Model ◽  
Investment Plan ◽  
Terminal Time ◽  
Variance Risk ◽  
Maximum Drawdown ◽  
Mean Variance

The objective of the continuous time mean-variance model is to minimize the variance (risk) of an investment portfolio with a given mean at the terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this problem, we consider to minimize the variances of the investment portfolio in the multi-time state. The advantage of this multi-time state mean-variance model is the minimization of the risk of the investment portfolio within the investment period. To obtain the optimal strategy of the model, we introduce a sequence of Riccati equations, which are connected by jump boundary conditions. In addition, we establish the relationships between the means and variances in the multi-time state mean-variance model. Furthermore, we use an example to verify that the variances of the multi-time state can affect the average of Maximum-Drawdown of the investment portfolio.

Optimal selection of financial risk investment portfolio based on random matrix method

2020 ◽  
Vol 20 (3) ◽  
pp. 859-868
Author(s):  
Jie Tian ◽  
Kun Zhao
Keyword(s):  
Covariance Matrix ◽  
Random Matrix ◽  
Financial Risk ◽  
Good Effect ◽  
Investment Portfolio ◽  
Variance Model ◽  
Minimum Risk ◽  
The Mean ◽  
Risk Investment ◽  
Mean Variance

The optimization of investment portfolio is the key to financial risk investment. In this study, the investment portfolio was optimized by removing the noise of covariance matrix in the mean-variance model. Firstly, the mean-variance model and noise in covariance matrix were briefly introduced. Then, the correlation matrix was denoised by KR method (Sharifi S, Grane M, Shamaie A) from random matrix theory (RMT). Then, an example was given to analyze the application of the method in financial stock investment portfolio. It was found that the stability of the matrix was improved and the minimum risk was reduced after denoising. The study of minimum risk under different M values and stock number suggested that calculating the optimal value of M and stock number based on RMT could achieve optimal financial risk investment portfolio result. It shows that RMT has a good effect on portfolio optimization and is worth promoting widely.

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 Last-Train Timetabling under Transfer Demand Uncertainty: Mean-Variance Model and Heuristic Solution

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Shuo Yang ◽  
Kai Yang ◽  
Ziyou Gao ◽  
Lixing Yang ◽  
Jungang Shi
Keyword(s):  
Demand Uncertainty ◽  
Risk Measure ◽  
Heuristic Solution ◽  
Variance Model ◽  
Train Timetabling ◽  
Subway System ◽  
Variance Risk ◽  
Demand Variability ◽  
Variance Risk Measure ◽  
Mean Variance

Traditional models of timetable generation for last trains do not account for the fact that decision-maker (DM) often incorporates transfer demand variability within his/her decision-making process. This study aims to develop such a model with particular consideration of the decision-makers’ risk preferences in subway systems under uncertainty. First, we formulate an optimization model for last-train timetabling based on mean-variance (MV) theory that explicitly considers two significant factors including the number of successful transfer passengers and the running time of last trains. Then, we add the mean-variance risk measure into the model to generate timetables by adjusting the last trains’ departure times and running times for each line. Furthermore, we normalize two heterogeneous terms of the risk measure to provide assistance in getting reasonable results. Due to the complexity of MV model, we design a tabu search (TS) algorithm with specifically designed operators to solve the proposed timetabling problem. Through computational experiments involving the Beijing subway system, we demonstrate the computational efficiency of the proposed MV model and the heuristic approach.

scholarly journals An Analysis of Cross-sectional Investment Portfolio with the Consideration of Risk and Return

2021 ◽  
Vol 235 ◽  
pp. 01036
Author(s):  
Jingzheng Luo ◽  
Jiasheng Guo ◽  
Hui Li
Keyword(s):  
Service Industry ◽  
Investment Portfolio ◽  
Cross Sectional ◽  
Variance Model ◽  
Car Industry ◽  
The Us ◽  
Trade War ◽  
Rational Investment ◽  
The Impact ◽  
Mean Variance

Recently, investors are requiring diversified options on the security investment, while the sudden incidents, such as the trade war and the pandemic of COVID-19, make the investment market more volatile and turbulent. Thus, this article will discuss how investors can make rational investment decisions by using the Markowitz’s portfolio theory and its Mean-Variance Model in the U.S. investment market, in order to meet the requirement of diversification and to earn relatively stable profit. Therefore, the data spanning from 2016 to 2020 is used to provide investors with more reliable and comprehensive investment information. Meanwhile, a novel cross-section portfolio is given to fulfill the diversified and innovative investment needs of investors. The industries included are car industry, biopharmaceutical industry and financial service industry. Furthermore, the results reflect the actual situation to a large extent, including the weakness in the US market in December 2018 due to uncertain Fed policy and the impact of the COVID-19 in 2020. In this article, an Intra-Industry analysis based on the net asset values of the three targeted industries will be carried out first, then the Macro analysis will be conducted based on the optimal portfolio of the three industries. A conclusion of the findings is included at the end of the article.

scholarly journals An HJB approach to a general continuous-time mean-variance stochastic control problem

2018 ◽  
Vol 26 (4) ◽  
pp. 225-234
Author(s):  
Georgios Aivaliotis ◽  
A. Yu. Veretennikov
Keyword(s):  
Dynamic Optimization ◽  
Continuous Time ◽  
Optimization Problem ◽  
Value Function ◽  
Dynamic Optimization Problem ◽  
Terminal Time ◽  
Diffusion Controlled ◽  
Time Component ◽  
Mean Variance ◽  
The Value Function

Abstract A general continuous mean-variance problem is considered for a diffusion controlled process where the reward functional has an integral and a terminal-time component. The problem is transformed into a superposition of a static and a dynamic optimization problem. The value function of the latter can be considered as the solution to a degenerate HJB equation either in the viscosity or in the Sobolev sense (after a regularization) under suitable assumptions and with implications with regards to the optimality of strategies. There is a useful interplay between the two approaches – viscosity and Sobolev.

scholarly journals Optimization of the Mean-Variance Model Investment Portfolio in Five Mining Stocks Traded on the IDX

2021 ◽  
Vol 2 (2) ◽  
pp. 64-70
Author(s):  
Guskenoly Fauziah
Keyword(s):  
Industrial Development ◽  
Raw Materials ◽  
Energy Resource ◽  
Optimization Method ◽  
Capital Allocation ◽  
Investment Portfolio ◽  
Variance Model ◽  
The Mean ◽  
Investment Portfolios ◽  
Mean Variance

The Mining and Energy sector is a major foreign exchange earner, provides the largest energy resource, and as an absorber of labor. In addition, most of the energy resources used in the Indonesian economy come from mining. namely oil and coal. Investment for mining and energy exploration in Indonesia needs to be a priority and continue to be encouraged to maintain the level of reserves as raw materials for future industrial development, including downstream. This study aims to measure the performance of investment portfolios in several stocks in the Mining and Energy sectors. The portfolio optimization method is carried out using the Mean-Variance model (Markowitz model). Based on the results of the analysis, it is obtained that the combination and proportion of capital allocation on several stocks in the formation of an investment portfolio that has better performance, where the optimum portfolio composition obtained a portfolio return of 0.000866205 with a portfolio variance of 0.000261104. In addition, the results of the analysis can be concluded that the return ratio can affect the model.

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