نمونه کارها تنظیم بهینه سازی با دارایی های اضافه شده هزینه های معاملات بر اساس تدابیر اعتبار

In response to changeful financial markets and investor’s capital, we discuss a portfolio adjusting problem with additional risk assets and a riskless asset based on credibility theory. We propose two credibilistic mean–variance portfolio adjusting models with general fuzzy returns, which take lending, borrowing, transaction cost, additional risk assets and capital into consideration in portfolio adjusting process. We present crisp forms of the models when the returns of risk assets are some deterministic fuzzy variables such as trapezoidal, triangular and interval types. We also employ a quadratic programming solution algorithm for obtaining optimal adjusting strategy. The comparisons of numeral results from different models illustrate the efficiency of the proposed models and the algorithm.

By assuming the lending and borrowing of money at a given riskless interest rate, Sharpe (1964) proposed the capital asset pricing model (CAPM). With the introduction of a riskless asset, an investor is able to put part of his or her money in riskless asset and the remainder in any of the risky portfolios contained in a feasible set. Sharpe et al. (1999) pointed out that adding these new opportunities expands the feasible set significantly and, more important, changes the location of a substantial part of an efficient set. The changes concern investors. Portfolio selection research, such as Best and Hlouskova (2000) and Zhang and Wang (2008), take the riskless asset into account and show a significant distinction between portfolio selection of only considering risk assets and portfolio selection of considering the existence of riskless asset.

In the paper, we consider the adjusting problem for an existing portfolio in response to changed financial markets and investors’ capital. By taking the returns of risk assets as fuzzy variables, we use the credibilistic expected value and credibilistic variance to measure the return and risk of the assets. We present the credibilistic mean–variance model for portfolio adjusting with transaction costs, additional risk assets and a riskless asset. The proposed models in this paper can be regarded as an extension of the model discussed in Zhang et al. (2010). Furthermore, the models based on credibilistic theory are more useful to describe an uncertain investment environment with vagueness and ambiguity than the Markowitz models (1952, 1959). Under the assumption that the return of risk assets are some deterministic fuzzy variables, we convert the optimization models into crisp forms and employ a quadratic programming solver for obtaining optimal solutions. We give a series of examples to illustrate the impact of inclusion of additional risk assets, a riskless asset with lending or borrowing and transaction cost in portfolio adjusting. The computational results show that an investor’s risk-aversion determines the amount of lending or borrowing in a riskless asset. The more conservative the investor is, the more lending he or she selects. The more aggressive the investor is, the more borrowing he or she selects.