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.

A DIRECT METHOD IN OPTIMAL PORTFOLIO AND CONSUMPTION CHOICE

In this paper we use a direct method to solve the optimal portfolio andconsumption choice problem in the security market for a specific case,in which theutility function is of a given homogenous form, i.e. the so-called CRRA case. The ideacomes from the completion technique ever used in LQ optimal control.

IMPROVED GENETIC ALGORITHM TO OPTIMAL PORTFOLIO WITH RISK CONTROL

A modified model of optimal investment port folio in a random market with risk constraints is presented. An improved genetic algorithm (GA) is proposed to solve this nonlinear optimal problem. The numerical simulation of a large-scale investment combination for Shanghai stock market shows that GA has the advantage of faster convergence and wider adaptability than traditional optimization algorithm. This result alsodemonstrates that the improved GA performs better than the basic GA.

Analysis of Optimal Portfolio with Different Utility Function

The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure （martingale measure） if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.

Optimal consumption-leisure, portfolio and retirement selection based on α-maxmin expected CES utility with ambiguity

This article studies optimal consumption-leisure, portfolio and retirement selection of an infinitely lived investor whose preference is formulated by a-maxmin expected CES utility which is to differentiate ambiguity and ambiguity attitude. Adopting the recursive multiple- priors utility and the technique of backward stochastic differential equations （BSDEs）, we transform the （^-maxmin expected CES utility into a classical expected CES utility under a new probability measure related to the degree of an investor＇s uncertainty. Our model investi- gates the optimal consumption-leisure-work selection, the optimal portfolio selection, and the optimal stopping problem. In this model, the investor is able to adjust her supply of labor flex- ibly above a certain minimum work-hour along with a retirement option. The problem can be analytically solved by using a variational inequality. And the optimal retirement time is given as the first time when her wealth exceeds a certain critical level. The optimal consumption-leisure and portfolio strategies before and after retirement are provided in closed forms. Finally, the distinctions of optimal consumption-leisure, portfolio and critical wealth level under ambiguity from those with no vagueness are discussed.

Optimal stopping investment in a logarithmic utility-based portfolio selection problem

Background:In this paper,we study the right time for an investor to stop the investment over a given investment horizon so as to obtain as close to the highest possible wealth as possible,according to a Logarithmic utility-maximization objective involving the portfolio in the drift and volatility terms.The problem is formulated as an optimal stopping problem,although it is non-standard in the sense that the maximum wealth involved is not adapted to the information generated over time.Methods:By delicate stochastic analysis,the problem is converted to a standard optimal stopping one involving adapted processes.Results:Numerical examples shed light on the efficiency of the theoretical results.Conclusion:Our investment problem,which includes the portfolio in the drift and volatility terms of the dynamic systems,makes the problem including multi-dimensional financial assets more realistic and meaningful.

Optimal Decision-Making of Trans-Provincial Electricity Market Subjects with Risks under Renewable Portfolio Standards

The randomness and uncertainty of renewable energy generation are expected to significantly change the optimal decision-making of trans-provincial electricity market subjects.Therefore,it is beneficial to optimize the interests of each of these subjects,considering the unpredictable risks of renewable energy under the renewable portfolio standards(RPS)and researching their effects on the optimal decision-making of transprovincial electricity market multi-subjects.First,we develop a trans-provincial trading market mechanism for renewable energy and clarify the electricity supply and demand relation and the green certificates supply and demand relation of trans-provincial electricitymarketmulti-subjects.Then,under the RPS,we construct a multi-subject game model of the power supply chain that recognizes the risks,and adopt the reverse induction method to discuss the optimum risk-taking judgment of each subject in the trans-provincial electricity market.Finally,we useMATLAB to verify the viability and efficacy of the proposed gamemodel,and obtain a certain reference value for the optimal decision-making of trans-provincial electricity market subjects.In summary,we consider the uncertainty risks of renewable energy under RPS,study the effects of the green certificate price and risk aversion coefficient in the RPS mechanism on the optimal decisionmaking of trans-provincial electricity market subjects,and obtain the changing trends of two different power products and those of different electricity market subjects under the influence of the green certificate price and risk aversion coefficient,which have a certain reference value for studying the factors affecting the optimal decision-making of trans-provincial electricity market subjects.

Optimal Investment Strategy in Safe-region on Consumption and Portfolio Problem

This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give the definition of safe-region for investment. Moreover, in order to obtain the target wealth as quickly as possible, using Bellman dynamic programming principle, we get the optimal investment strategy and corresponding necessary expected time. At last we give some numerical computations for a set of different parameters.

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 novel hybrid algorithm based on a harmony search and artificial bee colony for solving a portfolio optimization problem using a mean-semi variance approach

Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.

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.

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.

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 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.

The Constrained Mean-Semivariance Portfolio Optimization Problem with the Support of a Novel Multiobjective Evolutionary Algorithm

The paper addresses the constrained mean-semivariance portfolio optimization problem with the support of a novel multi-objective evolutionary algorithm (n-MOEA). The use of semivariance as the risk quantification measure and the real world constraints imposed to the model make the problem difficult to be solved with exact methods. Thanks to the exploratory mechanism, n-MOEA concentrates the search effort where is needed more and provides a well formed efficient frontier with the solutions spread across the whole frontier. We also provide evidence for the robustness of the produced non-dominated solutions by carrying out, out-of-sample testing during both bull and bear market conditions on FTSE-100.

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.

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.

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.

Application of Interval Valued Fuzzy Linear Programming for Stock Portfolio Optimization

In this paper, based on existing results, decision making about portfolio investment schemes is discussed, ordering method of fuzzy numbers of interval value is shown, corresponding auxiliary models are established and solutions are provided with theories of fuzzy mathematics, optimization theory and numerical calculation, etc. Then it applies software programming to solve the portfolio investment situation between investors in savings and four securities according to the established models. The result shows that investors can choose the risk coefficient that they can bear to reach the maximum value of expected returns. The greater the risk coefficient, the greater the income, the smaller the risk coefficient and the smaller the income. Investors can determine their own portfolio strategy according to their own conditions in order to meet their own interests.

An Alternative Method of Stochastic Optimization: The Portfolio Model

We provide a new simple approach to stochastic dynamic optimization. In doing so, we derive the existing (standard) results using a far simpler technique than the duality and the variational methods.