Since the financial markets are complex, sometimes the future security returns are represented mainly based on experts’ estimations due to lack of historical data. This paper proposes a semivariance method for diversified portfolio selection, in which the security returns are given subjective to experts’ estimations and depicted as uncertain variables. In the paper, three properties of the semivariance of uncertain variables are verified. Based on the concept of semivariance of uncertain variables, two types of mean-semivariance diversified models for uncertain portfolio selection are proposed. Since the models are complex, a hybrid intelligent algorithm which is based on 99-method and genetic algorithm is designed to solve the models. In this hybrid intelligent algorithm, 99-method is applied to compute the expected value and semivariance of uncertain variables, and genetic algorithm is employed to seek the best allocation plan for portfolio selection. At last, several numerical examples are presented to illustrate the modelling idea and the effectiveness of the algorithm.

Diversified models for portfolio selection based on uncertain semivariance

In practical engineering optimization problems (such as risk assessments), the parameters of the objective functions can be intervals because of noise and uncertainty; however, such problems cannot be solved by traditional multiobjective optimization methods. Yet, very little study has addressed interval multiobjective optimization methods compared to traditional multiobjective optimization methods. Therefore, a novel interval multiobjective optimization method called the Interval Cooperative Multiobjective Artificial Bee Colony Algorithm (ICMOABC) based on multiple populations for multiple objectives and interval credibility is proposed. Interval credibility is selected as the interval dominant method. Interval credibility is easy to combine with multiobjective optimization methods because it can describe the mean and width of intervals without increasing the dimension of the objective functions. The proposed algorithm has M single-objective optimization subpopulations updated by artificial bee colony algorithm, meaning it uses evolutionary resources more efficiently. In order to bring in diversity, the elitist learning strategy is used in the archive. The results of ICMOABC on various benchmark problems sets with different characteristics demonstrate its superior performance compared to some state-of-the-art algorithms.

Cooperative Artificial Bee Colony Algorithm With Multiple Populations for Interval Multiobjective Optimization Problems

The following sections are included:IntroductionPricing By ArbitrageSingle-Period Binomial Option PricingUsing Portfolio TheoryPseudo-ProbabilitiesUsing CCMP TheoryMulti-Period Binomial Option PricingPut-Call ParityEuropean, American and Asian OptionsRandom Walks and Brownian MotionExercisesBibliography

Option pricing i

Portfolio decision analysis: recent developments and future prospects

In an indeterminacy economic environment, experts’ knowledge about the returns of securities consists of much uncertainty instead of randomness. This paper discusses portfolio selection problem in uncertain environment in which security returns cannot be well reflected by historical data, but can be evaluated by the experts. In the paper, returns of securities are assumed to be given by uncertain variables. According to various decision criteria, the portfolio selection problem in uncertain environment is formulated as expected-variance-chance model and chance-expected-variance model by using the uncertainty programming. Within the framework of uncertainty theory, for the convenience of solving the models, some crisp equivalents are discussed under different conditions. In addition, a hybrid intelligent algorithm is designed in the paper to provide a general method for solving the new models in general cases. At last, two numerical examples are provided to show the performance and applications of the models and algorithm.

Uncertain programming models for portfolio selection with uncertain returns

Variance is substituted by semi-variance in Markowitz's portfolio selection model. For dynamic valuation on exploration and development projects, one period portfolio selection is extended to multi-period. In this article, a class of multi-period semi-variance exploration and development portfolio model is formulated originally. Besides, a hybrid genetic algorithm, which makes use of the position displacement strategy of the particle swarm optimiser as a mutation operation, is applied to solve the multi-period semi-variance model. For this class of portfolio model, numerical results show that the mode is effective and feasible.

A class of multi-period semi-variance portfolio for petroleum exploration and development

The competing strategies between OPEC (Organization of the Petroleum Exporting Countries) and non-OPEC producers make the oil supply market a complex system, and thus, it is very difficult to model and to make predictions. In this paper, we combine the macro-model based on game theory and micro-model to propose a new approach for forecasting oil supply. We take into account the microscopic behaviour in the clearing market and also use the game relationships to adjust oil supplies in our approach. For the supply model, we analyse and consider the different behaviour of non-OPEC and OPEC producers. According to our analysis, limiting the oil supply, and thus maintaining oil price, is the best strategy for OPEC in the low-price scenario, while the rising supply is the best strategy in the high-price scenario. No matter what the oil price is, the dominant strategy for non-OPEC producers is to increase their oil supply. In the high-price scenario, OPEC will try to deplete non-OPEC’s share in the oil supply mar...

Oil supply between OPEC and non-OPEC based on game theory

This article is concerned with continuous-time portfolio selection based on a safety-first criterion under discontinuous price processes (jump-diffusion processes). The solution of the corresponding Hamilton–Jacobi–Bellman equation of the problem is demonstrated. The analytical solutions are presented when there does not exist any riskless asset. Moreover, the problem is also discussed while there exists one riskless asset.

Continuous-time safety-first portfolio selection with jump-diffusion processes

A standard procedure for the evaluation of emergency impact is developed, concentrating on variation of the impact degree. A numerical method is presented in this paper. The concepts of impact depth and impact width are introduced to assess the impact degree, and both of which determine the evolution path of impact. Based on the variation pattern of impact depth, the evolution path could be divided into rising stage, plateau stage, and recession stage, and path of each stage could be expressed in terms of specified functions. The major goal of this procedure is to measure the emergency impact and make predictions for the consequences. In the case study, we applied this procedure to the analysis of the impact caused by 3.11 earthquake in Japan and demonstrated the algorithm's effectiveness and feasibility. Although this methodology shows improvement in quantitative analysis of the emergency impact, the accuracy of the impact path and the derivative effect of secondary derivative events are issues that yet to be further studied.

/pdf/a-class-of-numerical-algorithm-for-impact-degree-assessment-3momh627n0.pdf

A Class of Numerical Algorithm for Impact Degree Assessment of Emergency Systems

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Papers

A class of multi-period semi-variance portfolio for petroleum exploration and development

Oil supply between OPEC and non-OPEC based on game theory

Continuous-time safety-first portfolio selection with jump-diffusion processes

A Class of Numerical Algorithm for Impact Degree Assessment of Emergency Systems