nan Sukono

The application of genetic algorithm optimization on quadratic investment portfolio without a risk-free asset under Value-at-Risk

In this paper, we performed the Genetic Algorithm within problems of quadratic investment portfolio without a risk-free asset under Value-at-Risk. The limitation of this study is that the risk of an investment portfolio measured by Value-at-Risk, and each investor has the nature of risk aversion. To solve these problems: First, we established the mean vector and covariance matrix. The second step was to define the vector mean and covariance matrices for the formulation of Value-at-Risk of the investment portfolio. Third, using the mean vector and Value-at-Risk established the model. To complete the optimization problem, we performed the Genetic Algorithm. The results show that the trade-off between risk and expected return does not only depend on the type of investor but also on the size of the investment. The Genetic Algorithm certifies us the robust solution in the optimization problem because of its natural ability to locate the global minimal. Moreover, genetic algorithm can be used as an effective way in numerical completion of the optimization of quadratic investment portfolio. In a realistic investment situation, it has likely more constraints. For example, the restriction on short-selling, is need to be considered.

Numerical Simulation on Solving Three-Dimensional Global Optimization Problems in cooperation of Filled Function and Search Direction

Global optimization problem still becomes an interest due to the challenge of locating the global optimum of nonlinear objective function with multiple local minima. Two challenges on solving global optimization problem are; firstly how to reach the better minimizer from the current minimizer, and secondly how to decide that the obtained minimizer is the desired global minimizer. One of the recent considered deterministic easy applied methods, which concerned in the mentioned problems, is the filled function method. The basic concept of filled function method is to build such an auxiliary function to locate a point with lower function value than the current minimizer. One of the keys to the successfully filled function method is how to decide the search direction to reach and locate a better local minimizer. In this paper, a three-dimensional filled function method and its search direction are introduced. The algorithm is presented and implemented to some benchmark test function. The numerical performance of the method on solving three-dimensional global optimization problems is presented.

Solving Unconstrained Global Optimization Problem Using Parameter Free Filled Function in Cooperation with Jameson Gradient Based Method

Global optimization problem still becomes a challenges due to the problem on locating the global optimum of multimodal function. How to reach the better minimizer from the current minimizer and how to decide that the obtained minimizer is the desired one are both major challenges on solving global optimization problem. Filled function method is one of the recent considered deterministic easy applied methods which concerned to the mentioned problems. The basic concept of filled function method is firstly by minimizing the objective function (first phase) then to build such an auxiliary function which to be minimized (second phase) in order to locate a point with lower function value than the current minimizer of the objective function. In the second phase, a local minimization method can be applied. Newtons method is considered to be fast method on finding the zero of gradient of quadratic function, but may be very expensive or infeasible to determine the Hessian matrix in the case of complex problems. The Jameson gradient based method is the search procedures which avoid the need to store an estimate of the Hessian as well as its inverse and do not require exact line searches. In this paper, an algorithm in cooperation of parameter free filled function method and Jameson gradient method are introduced for solving global optimization problem with two variables. The algorithm is implemented to some benchmark test function. The numerical performance of the method on solving two-dimensional global optimization problems is presented.

Modeling of Mean-VaR portfolio optimization by risk tolerance when the utility function is quadratic

The problems of investing in financial assets are to choose a combination of weighting a portfolio can be maximized return expectations and minimizing the risk. This paper discusses the modeling of Mean-VaR portfolio optimization by risk tolerance, when square-shaped utility functions. It is assumed that the asset return has a certain distribution, and the risk of the portfolio is measured using the Value-at-Risk (VaR). So, the process of optimization of the portfolio is done based on the model of Mean-VaR portfolio optimization model for the Mean-VaR done using matrix algebra approach, and the Lagrange multiplier method, as well as Khun-Tucker. The results of the modeling portfolio optimization is in the form of a weighting vector equations depends on the vector mean return vector assets, identities, and matrix covariance between return of assets, as well as a factor in risk tolerance. As an illustration of numeric, analyzed five shares traded on the stock market in Indonesia. Based on analysis of five s...

Mean-Variance portfolio optimization by using non constant mean and volatility based on the negative exponential utility function

Investments in stocks investors are also faced with the issue of risk, due to daily price of stock also fluctuate. For minimize the level of risk, investors usually forming an investment portfolio. Establishment of a portfolio consisting of several stocks are intended to get the optimal composition of the investment portfolio. This paper discussed about optimizing investment portfolio of Mean-Variance to stocks by using mean and volatility is not constant based on the Negative Exponential Utility Function. Non constant mean analyzed using models Autoregressive Moving Average (ARMA), while non constant volatility models are analyzed using the Generalized Autoregressive Conditional heteroscedastic (GARCH). Optimization process is performed by using the Lagrangian multiplier technique. As a numerical illustration, the method is used to analyze some stocks in Indonesia. The expected result is to get the proportion of investment in each stock analyzed