Stochastic Optimization model

We need to create a stochastic optimization model (also known as optimal stopping problem, stochastic barrier model, dynamic stochastic optimization). The process is a simple Weiner process, and we need an optimization model (numeric or analytic) that tells us where the optimal entry point ("stopping criteria") is based on how the process changes. The criteria is that we must have chosen a point before the time has ended, as this will have a penalty. Consider the following: You must establish a long position in the market within an hour, and expect the price to move according to a wiener process. Each period is 5 minutes. At the end of each period, if price is better than we would expect it to be, we would enter position. The objective is to get in with a better price than the value at the end of all periods. As we get closer to the end, we also have a better idea of what the price will be. If we fail to enter the position before the time is up, we will get penalized. We have a few papers available on this with different methods, but lack the time to go through them hence we wish to outsource this little project. For someone with experience in stochastic optimization it shouldn't take longer than hour or two, but if you only have good math knowledge you can expect to spend some time on understanding the techniques first. Requirements: The model and it's assumption shall be explained in detail Simple code for how to us the model (c++, matlab, mathematica or even pseudo-code is fine) The model is correctly implemented, hence based on the stochastic process it is possible to run a simulation and verify the result (not included in your tasks, but we need to do it in order to pay you) More details will be provided later, but the above information explains the scope of the project.