Stochastic Optimization approaches for trading on financial and energy markets

The goal of this thesis is twofold. First, for a rather broad class of financial options a stochastic model predictive control (SMPC) approach is proposed for dynamically hedging a portfolio of underlying assets.After formulating the dynamic hedging problem as a stochastic control problem with a least-squares criterion, for plain vanilla and exotic options we test its ability to replicate the payoff at expiration date. We show not only that relatively small hedging errors are obtained in spite of price realizations, but also that the approach is robust with respect to market modeling errors. The SMPC approach is then extended to hedging derivative contracts (such as plain vanilla and exotic options) in the presence of transaction costs. After proving that the least-squares approach is no longer suitable to handle this kind of market, the hedging performance obtained by three different measures is tested and compared in simulation on a European call and a barrier option. The aim in the second part of this thesis is to present a novel market design for trading energy and regulating reserves and to introduce a strategy for the optimal bidding problem in such a scenario. In the deregulated market, the presence of several market participants or Balance Responsible Parties (BRPs) entitled for trading energy, together with the increasing integration of renewable sources and price-elastic loads, shift the focus on decentralized control and reliable forecast techniques. The main feature of the considered market design is its double-sided nature. In addition to portfolio-based supply bids and based on prediction of their stochastic production and load, BRPs are allowed to submit risk-limiting requests. Requesting capacity from the AS market corresponds to giving to the market an estimate of the possible deviation from the daily production schedule resulting from the day-ahead auction and from bilateral contracts, named E-Program. In this way each BRP is responsible for the balanced and safe operation of the electric grid. On the other hand, at each Program Time Unit (PTU) BRPs must also offer their available capacity under the form of bids. In this paper, a bidding strategy to the double-sided market is described, where the risk is minimized and all the constraints are fulfilled. The algorithms devised are tested in a simulation environment and compared to the current practice, where the double-sided auction is not contemplated. Results in terms of expected imbalances and reliability are presented.