Business Plan, financial and risk analysis from the start-up mathrix

Mathrix is an e-learning math website that will be launched in March 2016. This master thesis offered a unique chance to interact with experienced supervisors in venture capitalism and project investment. It could serve as guidelines for entrepreneurs who intend to raise funds. Starting with the company’s business plan, the thesis focuses on estimating the company’s value with its return on investment using three scenarios and taking into consideration the risks evolved.

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.