OPTIMAL CONTROL OF MARKOVIAN SWITCHING SYSTEMS WITH APPLICATIONS TO PORTFOLIO DECISIONS UNDER INFLATION

This article is concerned with a class of control systems with Markovian switching, in which an It5 formula for Markov-modulated processes is derived. Moreover, an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman （HJB） equation with Markovian switching is characterized. Then, through the generalized HJB equation, we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation. Thus, we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds. Finally, for the CRRA utility function, we explicitly give the optimal consumption and portfolio policies. Numerical examples are included to illustrate the obtained results.

Optimal Portfolio and Consumption Rule with a CIR Model Under HARA Utility

In the real-world environments,different individuals have different risk preferences.This paper investigates the optimal portfolio and consumption rule with a Cox–Ingersoll–Ross(CIR)model in a more general utility framework.After consumption,an individual invests his wealth into the financial market with one risk-free asset and multiple risky assets,where the short-term rate is driven by the CIR model and stock price dynamics are simultaneously influenced by random sources from both stochastic interest rate and stock market itself.The individual hopes to optimize their portfolios and consumption rules to maximize expected utility of terminal wealth and intermediate consumption.Risk preference of individual is assumed to satisfy hyperbolic absolute risk aversion(HARA)utility,which contains power utility,logarithm utility,and exponential utility as special cases.By using the principle of stochastic optimality and Legendre transform-dual theory,the explicit expressions of the optimal portfolio and consumption rule are obtained.The sensitivity of the optimal strategies to main parameters is analysed by a numerical example.In addition,economic implications are also presented.Our research results show that Legendre transform-dual theory is an effective methodology in dealing with the portfolio selection problems with HARA utility and interest rate risk can be completely hedged by constructing specific portfolios.

Stochastic Optimal Economic Growth Model with Natural Resources

The paper examines an economic growth problem how social planners reasonably open up and retain natural resources. The objective is to maximize the total expected discounted utility of comsumption. Social planners＇ optimal decision and optimal expected rates at the steady state are derived. At last, how productivity and productivity shock affect on the expected growth rate, consumption-resources ratio and the fraction of exploited resources, are analyzed.

Evolutionary Multi-objective Portfolio Optimization in Practical Context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.

A branch-and-bound algorithm for discrete multi-factor portfolio optimization model

In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities.

Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures

In this study,we analyze three portfolio selection strategies for loss-averse investors:semi-variance,conditional value-at-risk,and a combination of both risk measures.Moreover,we propose a novel version of the non-dominated sorting genetic algorithm II and of the strength Pareto evolutionary algorithm 2 to tackle this optimization problem.The effectiveness of these algorithms is compared with two alternatives from the literature from five publicly available datasets.The computational results indicate that the proposed algorithms in this study outperform the others for all the examined performance metrics.Moreover,they are able to approximate the Pareto front even in cases in which all the other approaches fail.

Take Bitcoin into your portfolio:a novel ensemble portfolio optimization framework for broad commodity assets

The emergence and growing popularity of Bitcoins have attracted the attention of the financial world.However,few empirical studies have considered the inclusion of the newly emerged commodity asset in the global commodity market.It is of great importance for investors and policymakers to take advantage of this asset and its potential benefits by incorporating it as a part of the broad commodity trading portfolio.In this study,we propose a novel ensemble portfolio optimization(NEPO)framework utilized for broad commodity assets,which integrates a hybrid variational mode decomposition-bidirectional long short-term memory deep learning model for future returns forecast and a reinforcement learning-based model for optimizing the asset weight allocation.Our empirical results indicate that the NEPO framework could effectively improve the prediction accuracy and trend prediction ability across various commodity assets from different sectors.In addition,it could effectively incorporate Bitcoins into the asset pool and achieve better financial performance compared to traditional asset allocation strategies,commodity funds,and indices.

Portfolio optimization of credit risky bonds: a semi-Markov process approach

This article presents a semi-Markov process based approach to optimally select a portfolio consisting of credit risky bonds.The criteria to optimize the credit portfolio is based on l_(∞)-norm risk measure and the proposed optimization model is formulated as a linear programming problem.The input parameters to the optimization model are rate of returns of bonds which are obtained using credit ratings assuming that credit ratings of bonds follow a semi-Markov process.Modeling credit ratings by semi-Markov processes has several advantages over Markov chain models,i.e.,it addresses the ageing effect present in the credit rating dynamics.The transition probability matrices generated by semi-Markov process and initial credit ratings are used to generate rate of returns of bonds.The empirical performance of the proposed model is analyzed using the real data.Further,comparison of the proposed approach with the Markov chain approach is performed by obtaining the efficient frontiers for the two models.

An improved portfolio optimization model for oil and gas investment selection

For oil company decision-makers,the principal concern is how to allocate their limited resources into the most valuable opportunities.Recently a new management philosophy,＂Beyond NPV＂,has received more and more international attention.Economists and senior executives are seeking effective alternative analysis approaches for traditional technical and economic evaluation methods.The improved portfolio optimization model presented in this article represents an applicable technique beyond NPV for doing capital budgeting.In this proposed model,not only can oil company executives achieve trade-offs between returns and risks to their risk tolerance,but they can also employ an ＂operational premium＂ to distinguish their ability to improve the performance of the underlying projects.A simulation study based on 19 overseas upstream assets owned by a large oil company in China is conducted to compare optimized utility with non-optimized utility.The simulation results show that the petroleum optimization model including ＂operational premium＂ is more in line with the rational investors＇ demand.

Matrix decomposition and Lagrangian dual method for discrete portfolio optimization under concave transaction costs

In this paper, the discrete mean-variance model is considered for portfolio selection under concave transaction costs. By using the Cholesky decomposition technique, the convariance matrix to obtain a separable mixed integer nonlinear optimization problem is decomposed. A brand-and-bound algorithm based on Lagrangian relaxation is then proposed. Computational results are reported for test problems with the data randomly generated and those from the US stock market.

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.

Stressed portfolio optimization with semiparametric method

Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.

Discovering optimal weights in weighted‑scoring stock‑picking models: a mixture design approach

Certain literature that constructs a multifactor stock selection model adopted a weighted-scoring approach despite its three shortcomings.First,it cannot effectively identify the connection between the weights of stock-picking concepts and portfolio performances.Second,it cannot provide stock-picking concepts’optimal combination of weights.Third,it cannot meet various investor preferences.Thus,this study employs a mixture experimental design to determine the weights of stock-picking concepts,collect portfolio performance data,and construct performance prediction models based on the weights of stock-picking concepts.Furthermore,these performance prediction models and optimization techniques are employed to discover stock-picking concepts’optimal combination of weights that meet investor preferences.The samples consist of stocks listed on the Taiwan stock market.The modeling and testing periods were 1997–2008 and 2009–2015,respectively.Empirical evidence showed(1)that our methodology is robust in predicting performance accurately,(2)that it can identify significant interactions between stock-picking concepts’weights,and(3)that which their optimal combination should be.This combination of weights can form stock portfolios with the best performances that can meet investor preferences.Thus,our methodology can fill the three drawbacks of the classical weighted-scoring approach.

Optimization of Pension Asset Portfolio in Nigeria with Contributors’ Specified Return Rate

This work focuses on the optimization of investment contributions of pension asset with a view to improving contributors’ participation in achieving better return on investment (RoI) of their funds. We viewed some new regulations on Nigeria’s Contributory Pension Scheme” (CPS) from amended legislation of 2014, some of which are yet to be implemented when their regulations are approved. A mathematical model involving 5 variables, 5 inequality constraints covering regulatory limitations and limitation on scarce resource known as Asset Under Management (AUM), suggested and mathematically shown to be possible through “maximization of return irrespective of risk” while obeying all regulatory controls as our constraints optimized. Optimized portfolio using MatLab shows that the portfolio representing AES 2013 portfolio with a deficit growth of 15.75 m representing 3.27% less than the portfolio’s full growth potential within defined assumptions would have been averted if contributors actually set their targets and investment managers optimize from forecasts of future prices using trend analysis.

Forward robust portfolio selection: The binomial case

We introduce a new approach for optimal portfolio choice under model ambiguity by incorporating predictable forward preferences in the framework of Angoshtari et al.[2].The investor reassesses and revises the model ambiguity set incrementally in time while,also,updating his risk preferences forward in time.This dynamic alignment of preferences and ambiguity updating results in time-consistent policies and provides a richer,more accurate learning setting.For each investment period,the investor solves a worst-case portfolio optimization over possible market models,which are represented via a Wasserstein neighborhood centered at a binomial distribution.Duality methods from Gao and Kleywegt[10];Blanchet and Murthy[8]are used to solve the optimization problem over a suitable set of measures,yielding an explicit optimal portfolio in the linear case.We analyze the case of linear and quadratic utilities,and provide numerical results.

A Novel Smart Beta Optimization Based on Probabilistic Forecast

Rule-based portfolio construction strategies are rising as investmentdemand grows, and smart beta strategies are becoming a trend amonginstitutional investors. Smart beta strategies have high transparency, lowmanagement costs, and better long-term performance, but are at the risk ofsevere short-term declines due to a lack of Risk Control tools. Although thereare some methods to use historical volatility for Risk Control, it is still difficultto adapt to the rapid switch of market styles. How to strengthen the RiskControl management of the portfolio while maintaining the original advantagesof smart beta has become a new issue of concern in the industry. Thispaper demonstrates the scientific validity of using a probability prediction forposition optimization through an optimization theory and proposes a novelnatural gradient boosting (NGBoost)-based portfolio optimization method,which predicts stock prices and their probability distributions based on non-Bayesian methods and maximizes the Sharpe ratio expectation of positionoptimization. This paper validates the effectiveness and practicality of themodel by using the Chinese stock market, and the experimental results showthat the proposed method in this paper can reduce the volatility by 0.08 andincrease the expected portfolio cumulative return (reaching a maximum of67.1%) compared with the mainstream methods in the industry.

COVID‑19 pandemic and the crude oil market risk:hedging options with non‑energy financial innovations

This study examines the hedging effectiveness of financial innovations against crude oil investment risks,both before and during the COVID-19 pandemic.We focus on the non-energy exchange traded funds(ETFs)as proxies for financial innovations given the potential positive correlation between energy variants and crude oil proxies.We employ a multivariate volatility modeling framework that accounts for important statistical features of the non-energy ETFs and oil price series in the computation of optimal weights and optimal hedging ratios.Results show evidence of hedging effectiveness for the financial innovations against oil market risks,with higher hedging performance observed during the pandemic.Overall,we show that sectoral financial innovations provide resilient investment options.Therefore,we propose that including the ETFs in an investment portfolio containing oil could improve risk-adjusted returns,especially in similar financial crisis as witnessed during the pandemic.In essence,our results are useful for investors in the global oil market seeking to maximize risk-adjusted returns when making investment decisions.Moreover,by exploring the role of structural breaks in the multivariate volatility framework,our attempts at establishing robustness for the results reveal that ignoring the same may lead to wrong conclusions about the hedging effectiveness.

NECESSARY AND SUFFICIENT CONDITION FOR THE EXISTENCE OF A NONNEGATIVE EQUILIBRIUM PRICE VECTOR IN THE CAPITAL MARKET WITH SHORT-SELLING

For the capital market satisfying standard assumptions that are widely adopted in the equilibrium analysis,a necessary and sufficient condition for the existence and uniqueness of a nonnegative equilibrium price vector that clears the mean-variance capital market with short sale allowed is derived.Moreover,the given explicit formula for the equilibrium price shows clearly the relationship between prices of assets and statistical properties of the rate of return on assets,the desired rates of return of individual investors as well as other economic quantities.The economic implication of the derived condition is briefly discussed.These results improve the available results about the equilibrium analysis of the mean-variance market.

Optimal Consumption, Leisure and Job Choice under Inflationary Environment

The optimal job choice,consumption and portfolio decision-making of economic agents under inflationary environment for a continuous infinite time are studied.The agent’s preference is characterized by the Cobb-Douglas utility function with two variables of consumption and leisure.The economic agent invests in three kinds of assets:risk-free bonds,inflation index bonds and risky assets.The agent has two kinds of working conditions:One is the work with high income and little leisure time,and the other is the work with low income and much leisure time.Firstly,the real wealth process after inflation discount is derived by using Itôformula.Then,based on the expected utility maximization standard under any working state,martingale method is adopted to obtain the closed form solution of optimal job choice,consumption and portfolio decision-making.Finally,the effects of wealth and inflation volatility on the optimal consumption and portfolio strategies are quantitatively analyzed by numerical simulation with given parameters.

I_(ϵ+)LGEA:A Learning-Guided Evolutionary Algorithm Based on I_(ϵ+) Indicator for Portfolio Optimization

Portfolio optimization is a classical and important problem in the field of asset management,which aims to achieve a trade-off between profit and risk.Previous portfolio optimization models use traditional risk measurements such as variance,which symmetrically delineate both positive and negative sides and are not practical and stable.In this paper,a new model with cardinality constraints is first proposed,in which the idiosyncratic volatility factor is used to replace traditional risk measurements and can capture the risks of the portfolio in a more accurate way.The new model has practical constraints which involve the sparsity and irregularity of variables and make it challenging to be solved by traditional Multi-Objective Evolutionary Algorithms(MOEAs).To solve the model,a Learning-Guided Evolutionary Algorithm based on I_(ϵ+)indicator(I_(ϵ+)LGEA)is developed.In I_(ϵ+)LGEA,the I_(ϵ+)indicator is incorporated into the initialization and genetic operators to guarantee the sparsity of solutions and can help improve the convergence of the algorithm.And a new constraint-handling method based on I_(ϵ+)indicator is also adopted to ensure the feasibility of solutions.The experimental results on five portfolio trading datasets including up to 1226 assets show that I_(ϵ+)LGEA outperforms some state-of-the-art MOEAs in most cases.