This study aimed to predict the JKII (Jakarta Islamic Index) price as a index of sharia stocks and loss risk. uses geometric Brownian motion (GBM) Value at Risk (VaR; with Monte Carlo Simulation approach) on daily closing from 1 August 2020–13 2021 risk 16 2021–23 2021. The findings this were very accurate for predicting MAPE value 2.03%. Then, using VaR approach, prediction (one-day trading pe...

A mathematical model to price convertible bonds involving mixed fractional Brownian motion with jumps is presented. We obtain a general pricing formula using the risk neutral pricing principle and quasi-conditional expectation. The sensitivity of the price to changing various parameters is discussed. Theoretical prices from our jump mixed fractional Brownian motion model are compared with the p...

Classical Merton model assumes that an asset is modelled by Brownian motion or geometric Brownian motion. However, these models lack some empirical properties of usual financial series. If jumps are allowed into the model, it becomes much more appropriate. In this note, jump processes are briefly introduced. Subsequently, the impact of jumps on the optimal consumption and portfolio choice is st...

We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a version of the RayKnight theorem on local times. In our case, however, t...

A competitive firm which chooses the timing of investment and optimal volume of debt is considered. The price of the firm’s output follows the geometric Brownian motion or more general jump-diffusion processes, and the firm takes an arbitrage free borrowing rate as given. The optimal timing of investment and volume of debt is computed, and it is shown that if the borrowing rate is close to the ...

After analyzing the uncertainty of technology innovation diffusion (TID), this paper proposes the model of enterprises’ TID based on geometric Brownian motion with jump, and analyzes the optional timing and influence of adopting innovation technology on TID by each parameter. The results show that enterprise should immediately adopts the technology when its market demand is greater than the opt...

this article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (mhd) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. the model used for the nanofluid incorporates the effects of brownian motion and thermophoresis in the presence of thermal radiation. the skin-friction coefficient, nusselt number an...