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Chengming Xu - One of the best experts on this subject based on the ideXlab platform.

  • on the decomposition of the ruin probability for a jump diffusion surplus process compounded by a Geometric Brownian Motion
    The North American Actuarial Journal, 2006
    Co-Authors: Chengming Xu
    Abstract:

    Abstract If one assumes that the surplus of an insurer follows a jump-diffusion process and the insurer would invest its surplus in a risky asset, whose prices are modeled by a Geometric Brownian Motion, the resulting surplus for the insurer is called a jump-diffusion surplus process compounded by a Geometric Brownian Motion. In this resulting surplus process, ruin may be caused by a claim or oscillation. We decompose the ruin probability in the resulting surplus process into the sum of two ruin probabilities: the probability that ruin is caused by a claim, and the probability that ruin is caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When claim sizes are exponentially distributed, asymptotical formulas of the ruin probabilities are derived from the integro-differential equations, and it is shown that all three ruin probabilities are asymptotical power functions with the same orders and that the orders of the power functions are determined by the drift and...

Maheran Mohd Jaffar - One of the best experts on this subject based on the ideXlab platform.

  • forecasting value at risk of foreign exchange rate by integrating Geometric Brownian Motion
    Soft Computing, 2018
    Co-Authors: Siti Noorfaera Karim, Maheran Mohd Jaffar
    Abstract:

    Foreign exchange is one of the most important financial assets for all countries around the world including Malaysia. After recovering from the Asian financial crisis, Malaysia tried to build a strong currency in order to maintain the economic performance. The study focuses on Malaysia foreign exchange rate and foreign exchange risk between ten currencies, which are CNY, SGD, JPY, EUR, USD, THB, KRW, IDR, TWD and AUD. Unpredictability of the foreign exchange rate makes the traders hard to forecast the future rate and the future risk. The study implements the parametric approach in the Value at Risk (VaR) method and the Geometric Brownian Motion (GBM) model. The objectives of the study are to integrate the VaR model with the GBM model in order to compute or forecast the VaR. By using parametric approach, the study successfully computes the VaR of foreign exchange rate for different confidence levels. The GBM model is suitable to forecast the foreign exchange rate accurately using less than one year input data and using the log volatility formula. Lastly, the study verifies the feasibility of the integrated model for a one month holding period using the data shifting technique. In conclusion, the prediction of future foreign exchange rate and foreign exchange risk is important in order to know the performance of a country and to make better decision on investment.

  • SCDS - Modeling and Forecasting Mudharabah Investment with Risk by Using Geometric Brownian Motion
    Communications in Computer and Information Science, 2016
    Co-Authors: Nurizzati Azhari, Maheran Mohd Jaffar
    Abstract:

    This study developed mudharabah investment with risk model by considering the rate of return as a total of deterministic profit rate and a function of white noise that is Geometric Brownian Motion. The result shows that the investment is considered as accurately forecast when using this developed model. The profit from mudharabah investment is compared with single party investment. The result obtained shows that the profit difference between mudharabah investment and single party investment is very small. It is verified that the developed model can be used in forecasting the investment and profit for two parties.

  • forecasting share prices of small size companies in bursa malaysia using Geometric Brownian Motion
    Applied Mathematics & Information Sciences, 2014
    Co-Authors: Siti Nazifah Zainol Abidin, Maheran Mohd Jaffar
    Abstract:

    This paper proposes a way to forecast the future closing price of small sized companies by using Geometric Brownian Motion. Forecasting is restricted to short term investment because most of the investors aim to gain profit in short period of time. This study focusses on small sized companies because the asset prices are lower, hence the asset are affordable for all level of investors. But, to choose the suitable counters to invest is difficult and with the uncertain ty of market prices, it will lead to the decline of the investor's confidence level. Therefore, forecasting future closing p rice is essential. In this paper, we suggest that Geometric Brownian Motion which involves randomness, volatility and drift can be used to forecast a maximum of two week investment closing prices. This method is accurately proven by the lower value of the Mean Absolute Percentage Error (MAPE). In addition, the uses of data is also investigated and found that one week data is enough to forecast the share prices using Geometric Brownian Motion.

  • a review on Geometric Brownian Motion in forecasting the share prices in bursa malaysia
    2012
    Co-Authors: Siti Nazifah, Zainol Abidin, Maheran Mohd Jaffar, Selangor Darul Ehsan
    Abstract:

    The application of Geometric Brownian Motion to forecast share prices is reviewed. Formula of Geometric Brownian Motion is analyzed and examined to meet the fluctuation of share prices. Uncertainty and unpredictability share prices makes it difficult for investors to forecast future prices . Thus, this reviewed paper aims to state the importance of application of Geometric Brownian Motion into share prices and helps the investors to forecast future prices for the short-term investment. This paper will elaborate Geometric Brownian Motion involving the randomness, volatility and drift that can help investors in making their investment decision wisely.

  • comparative analysis of Geometric Brownian Motion model in forecasting fbmhs and fbmklci index in bursa malaysia
    IEEE Symposium on Business Engineering and Industrial Applications, 2011
    Co-Authors: Aslina Omar, Maheran Mohd Jaffar
    Abstract:

    On April 17, 1999, the Kuala Lumpur Stock Exchange, today known as Bursa Malaysia, launched a new index called Syariah Index (SI) to facilitate participation in the equity investment in accordance with Islamic syariah's principles. Syariah-based equity is basically shares of the company meeting the criteria of Islamic jurisprudence. Indices are used as a performance benchmark for portfolios such as mutual fund shares. The index is a device that allows investors to measure the performance of the group share of the market. This paper forecasts the FTSE Bursa Malaysia Hijrah Shariah (FBMHS) and FTSE Bursa Malaysia KLCI (FBMKLCI) index using the better model of Geometric Brownian Motion in terms of volatility models and number of data. This paper shows that forecasting using log volatility and 4 week daily data gives accurate forecasting.

Masamitsu Ohnishi - One of the best experts on this subject based on the ideXlab platform.

  • an impulse control of a Geometric Brownian Motion with quadratic costs
    European Journal of Operational Research, 2006
    Co-Authors: Masamitsu Ohnishi, Motoh Tsujimura
    Abstract:

    We examine an optimal impulse control problem of a stochastic system whose state follows a Geometric Brownian Motion. We suppose that, when an agent intervenes in the system, it requires costs consisting of a quadratic form of the system state. Besides the intervention costs, running costs are continuously incurred to the system, and they are also of a quadratic form. Our objective is to find an optimal impulse control of minimizing the expected total discounted sum of the intervention costs and running costs incurred over the infinite time horizon. In order to solve this problem, we formulate it as a stochastic impulse control problem, which is approached via quasi-variational inequalities (QVI). Under a suitable set of sufficient conditions on the given problem parameters, we prove the existence of an optimal impulse control such that, whenever the system state reaches a certain level, the agent intervenes in the system. Consequently it instantaneously reduces to another level.

  • an optimal stopping problem for a Geometric Brownian Motion with poissonian jumps
    Mathematical and Computer Modelling, 2003
    Co-Authors: Masamitsu Ohnishi
    Abstract:

    This paper examines an optimal stopping problem for a Geometric Brownian Motion with random jumps. It is assumed that jumps occur according to a time-homogeneous Poisson process and the proportions of these sizes are independent and identically distributed nonpositive random variables. The objective is to find an optimal stopping time of maximizing the expected discounted terminal reward which is defined as a nondecreasing power function of the stopped state. By applying the ''smooth pasting technique'' [1,2], we derive almost explicitly an optimal stopping rule of a threshold type and the optimal value function of the initial state. That is, we express the critical state of the optimal stopping region and the optimal value function by formulae which include only given problem parameters except an unknown to be uniquely determined by a nonlinear equation.

Maciej Wiśniewolski - One of the best experts on this subject based on the ideXlab platform.

  • k hartman watson distributions a study on distributional dependencies between functionals of Geometric Brownian Motion gig and hartman watson distributions
    Journal of Mathematical Analysis and Applications, 2020
    Co-Authors: Maciej Wiśniewolski
    Abstract:

    Abstract The new general results for Brownian Motion functionals are obtained by introducing the so called K-transforms of the special function u. The transforms lead to the new distributions called here K-Hartman-Watson distributions. They are counterparts to the classical Hartman-Watson distributions, but with respect to the state-space variable. It is shown that the distribution of Geometric Brownian Motion e B t and its additive functional A t are described by the composition of General Inverse Gaussian (GIG) distribution with K-Hartman-Watson distribution. As a consequence two distributional dependencies are presented: the first between the distribution of GIG distribution on R + and the distribution of functional A t , and the second one, between the distribution of GIG on a hyperplane and the distribution of the vector ( A t , e B t ) .

Paulo Picchetti - One of the best experts on this subject based on the ideXlab platform.

  • Geometric Brownian Motion and structural breaks in oil prices a quantitative analysis
    Energy Economics, 2006
    Co-Authors: Fernando Antonio Slaibe Postali, Paulo Picchetti
    Abstract:

    The purpose of this paper is to present a quantitative analyses of oil price's path. We try to argue that, despite its parsimony and simplicity, Geometric Brownian Motion can perform well as a proxy for the movement of oil prices and for a state variable to evaluate oil deposits. We base our argument on evidences of very low speed of mean reverting (or long half-life), since unit root tests only can reject its null hypothesis in a sample longer than 100 years. On the other hand, we reject the null hypothesis of unit root with two endogenous breaks, showing that the usual rejection can be attributed to omitted structural breaks. We conclude that the average half-life of oil price (between 4 and 8 years depending on the model chosen) is long enough to allow a good approximation as a Geometric Brownian Motion.