exchange rate prediction, as one of the main variables in macroeconomics, has been one of the aims of the economic research for a long time. for modeling and predicting exchange rate we apply stochastic differential equation, specifically we use geometric brownian motion (gbm) and jump-diffusion process (mjdp) attributed to merton. we show that the result of simulation based on gbm and mjdp out...

This research studies three mathematical models, namely geometric Brownian motion (GBM), fractional (GFBM) model which was developed by adding the Hurst parameter to GBM characterize long-memory phenomenon, and Merton jump-diffusion (MJD) captures shocks via GBM. study sets out forecast Malaysia rubber prices for six months period beginning in January 2022 ending June 2022, involves four main s...

Real options theory suggests that managerial flexibility embedded within irreversible investments can account for a significant value in project valuation. Although the argument has become the dominant focus of capital investment theory over decades, yet recent survey literature in capital budgeting indicates that corporate practitioners still do not explicitly apply real options in investment ...

Asset prices are typically modeled with the geometric Brownian motion (GBM). Correlation between the assets is exogenously modeled and then ad-hoc assigned to the asset prices. This is conceptually and mathematically unsatisfying. We create a new, simple approach, which simultaneously models stochastic volatility and stochastic correlation. This approach replicates the realworld volatility – co...

The application of the model geometric Brownian motion (GBM) for problem modeling and forecasting prices cryptocurrencies is analyzed. For prediction solution stochastic differential equation GBM used, which has a linear drift diffusion coefficients. Different scenarios price movement are considered.
 Keywords: (GBM), modeling, forecasting, cryptocurrency.

Jump diffusion processes are often used as an alternative to geometric Brownian motion within continuous–time dynamic financial time series models. The advantages of the jump diffusion process are that it can not only account for discrete jumps in the path of the process, but it also provides a simple way of replacing the Gaussian return distributions that arise in geometric Brownian motion mod...

We consider a renewal jump-diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin probabilities and related quantities, in models with light...