Grant: Discovery Grants Program - Individual

In this research proposal, we focus mostly on optimization problems whose goals are to minimize the risk of an investor aiming to achieve, on average, a given return on investment. We postulate a market environment in which the investor is allowed to continuously rebalance his portfolio of stocks upon observation of the market evolution. The research avenues that we propose are all motivated by a desire to bring more realism into the modeling of this risk-return tradeoff problem. An idea crucial to this proposal is that of duality. When confronted with a challenging optimization problem, the duality approach creates an alternative related optimization problem, called the dual problem, which is typically simpler than the original problem. The solution to the relatively easier dual problem is then used to construct a solution for the original problem of interest. We will apply this idea, but in a way that differs from applications typically found in the current mathematical finance literature by being more systematic and algorithmic.