E jurnal Matematika

1-6

Authors: Ni Kadek Mayuliana, Eka N. Kencana, Luh Putu Ida Harini

Genetic algorithm is a part of heuristic algorithm which can be applied to solve various computational problems. This work is directed to study the performance of the genetic algorithm (GA) to solve Multi Traveling Salesmen Problem (multi-TSP). GA is simulated to determine the shortest route for 5 to 10 salesmen who travelled 10 to 30 cities. The performance of this algorithm is studied based on the minimum distance and the processing time required for 10 repetitions for each of cities-salesmen combination. The result showed that the minimum distance and the processing time of the GA increase consistently whenever the number of cities to visit increase. In addition, different number of sales who visited certain number of cities proved significantly affect the running time of GA, but did not prove significantly affect the minimum distance.

15-21

Authors: Aulia Atika Prawibta Suharto, Komang Dharmawan, I Wayan Sumarjaya

Value at Risk explains the magnitude of the worst losses occurred in financial products investments with a certain level of confidence and time interval. The purpose of this study is to estimate the VaR of portfolio using Archimedean Copula family. The methods for calculating the VaR are as follows: (1) calculating the stock return; (2) calculating descriptive statistics of return; (3) checking for the nature of autocorrelation and heteroscedasticity effects on stock return data; (4) checking for the presence of extreme value by using Pareto tail; (5) estimating the parameters of Achimedean Copula family; (6) conducting simulations of Archimedean Copula; (7) estimating the value of the stock portfolio VaR. This study uses the closing price of TLKM and GGRM. At 90% the VaR obtained using Clayton, Gumbel, Frank copulas are 0.9562%, 1.0189%, 0.9827% respectively. At 95% the VaR obtained using Clayton, Gumbel, Frank copulas are 1.2930%, 1.2522%, 1.3152% respectively. At 99% the VaR obtained using Clayton, Gumbel, Frank copulas are 2.0327%, 1.9164%, is 1.8678% respectively. In conclusion estimation of VaR using Clayton copula yields the highest VaR.

29-36

Authors: Ni Nyoman Ayu Artanadi, Komang Dharmawan, Ketut Jayanegara

Option is a contract between the writer and the holder which entitles the holder to buy or sell an underlying asset at the maturity date for a specified price known as an exercise price. Asian option is a type of financial derivatives which the payoff taking the average value over the time series of the asset price. The aim of the study is to present the Monte Carlo-Control Variate as an extension of Standard Monte Carlo applied on the calculation of the Asian option price. Standard Monte Carlo simulations 10.000.000 generate standard error 0.06 and the option price convergent at Rp.160.00 while Monte Carlo-Control Variate simulations 100.000 generate standard error 0.01 and the option price convergent at Rp.152.00. This shows the Monte Carlo-Control Variate achieve faster option price toward convergent of the Monte Carlo Standar.

47-55

Authors: Ni Luh Putu Ratna Kumalasari, Ni Luh Putu Suciptawati, Made Susilawati

Outliers are observations that are far away from other observations. Outlier can be interfered with the process of data analysis which influence the regression parameters estimation.Methods that are able to deal with outliers are Minimum Covariance Determinant and Least Absolute Deviation methods. However, if both methods are applied with small sample the validity of both methods is being questioned. This research applies bootstrap to MCD and LAD methods to small sample. Resampling using 500, 750,and 1000 with confidence interval of 95% and 99% shows that both methods produce an unbiased estimators at 10%, 15%, and 20% outliers. The confidence interval of MCD-Bootstrap method is shorter than LAD-Bootstrap method. Both are, MCD-Bootstrap method is a better thus than LAD-Bootstrap method.

65-73

Authors: Ni Wayan Merry Nirmala Yani, I Gusti Ayu Made Srinadi, I Wayan Sumarjaya

Semiparametric regression is a regression model that includes parametric components and nonparametric components in a model. The regression model in this research is truncated spline semiparametric regression with case studies of patients with Dengue Hemorrhagic Fever (DHF) at Puri Raharja Hospital during the period of January to March 2015. The best regression model estimation is obtained from the selection of optimal knots which has minimum Generalized Cross Validation (GCV) is. Parametric components in this research include age (years), body temperature (0C), platelets (×〖10〗^3/μL), and hematocrit (%) as a nonparametric component. The minimum value of GCV is 0.03552045 achieved at the point of 39.6 knots, MSE value of 0.0296922; and the value of coefficient determination is 98.91%, obtained from semiparametric regression model truncated linear spline (order 2) with a single point of knots.

83-89

Authors: Laily A.A. Arifianti, K. Jayanegara, G.K. Gandhiadi, Eka N. Kencana

Family or domestic violence is meant as a pattern of someone behavior that abuse his/or her power against another member(s) in a family or domestic setting. Knowing the underlying factors that trigger family violence are important to keep family members form a harmonious relationship. This work is aimed to elaborate those factors. By analyzing primary data from 120 respondents whom witness and well informed about family violence in their neighborhoods, factor analyzes is applied. Data are collected by using tested questionnaires. The results showed they were six underlying factors for family violence with total accounted for all factors were 65.19 percent. Those factors are (a) social relationship, (b) job description, (c) past experience, (d) supporting factor, (e) economics’ status, and (f) harmonious relationship level. From these factors, social relationship dominates the others with variance explained for family violence as much as 21.39 percent.