Tightness and duality of martingale transport on the Skorokhod space

The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which turns out to be the corresponding Kantorovich dual. In this paper we consider the continuous-time martingale transport on the Skorokhod space of cadlag paths. Similar to the classical setting of optimal transport, we introduce different dual problems and establish the corresponding dualities by a crucial use of the S-topology and the dynamic programming principle

Comparison of a Heuristic Dynamic Programming and a Dual Heuristic Programming Based Adaptive Critics Neurocontroller for a Turbogenerator

This paper presents the design of a neurocontroller for a turbogenerator that augments/replaces the conventional automatic voltage regulator and the turbine governor. The neurocontroller uses a novel technique based on the adaptive critic designs with emphasis on heuristic dynamic programming (HDP) and dual heuristic programming (DHP). Results are presented to show that the DHP based neurocontroller is robust and performs better than the HDP based neurocontroller, as well as the conventional controller, especially when the system conditions and configuration changes

Comparison of Heuristic Dynamic Programming and Dual Heuristic Programming Adaptive Critics for Neurocontrol of a Turbogenerator

This paper presents the design of an optimal neurocontroller that replaces the conventional automatic voltage regulator (AVR) and the turbine governor for a turbogenerator connected to the power grid. The neurocontroller design uses a novel technique based on the adaptive critic designs (ACDs), specifically on heuristic dynamic programming (HDP) and dual heuristic programming (DHP). Results show that both neurocontrollers are robust, but that DHP outperforms HDP or conventional controllers, especially when the system conditions and configuration change. This paper also shows how to design optimal neurocontrollers for nonlinear systems, such as turbogenerators, without having to do continually online training of the neural networks, thus avoiding risks of instability

Robust pricing--hedging duality for American options in discrete time financial markets

We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we consider an abstract setting, which includes the classical case with a fixed reference probability measure as well as the robust framework with a non-dominated family of probability measures. Our first insight is that by considering a (universal) enlargement of the space, we can see American options as European options and recover the pricing-hedging duality, which may fail in the original formulation. This may be seen as a weak formulation of the original problem. Our second insight is that lack of duality is caused by the lack of dynamic consistency and hence a different enlargement with dynamic consistency is sufficient to recover duality: it is enough to consider (fictitious) extensions of the market in which all the assets are traded dynamically. In the second part of the paper we study two important examples of robust framework: the setup of Bouchard and Nutz (2015) and the martingale optimal transport setup of Beiglb\"ock et al. (2013), and show that our general results apply in both cases and allow us to obtain pricing-hedging duality for American options.Comment: 29 page

Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

Dynamic Robust Transmission Expansion Planning

Recent breakthroughs in Transmission Network Expansion Planning (TNEP) have demonstrated that the use of robust optimization, as opposed to stochastic programming methods, renders the expansion planning problem considering uncertainties computationally tractable for real systems. However, there is still a yet unresolved and challenging problem as regards the resolution of the dynamic TNEP problem (DTNEP), which considers the year-by-year representation of uncertainties and investment decisions in an integrated way. This problem has been considered to be a highly complex and computationally intractable problem, and most research related to this topic focuses on very small case studies or used heuristic methods and has lead most studies about TNEP in the technical literature to take a wide spectrum of simplifying assumptions. In this paper an adaptive robust transmission network expansion planning formulation is proposed for keeping the full dynamic complexity of the problem. The method overcomes the problem size limitations and computational intractability associated with dynamic TNEP for realistic cases. Numerical results from an illustrative example and the IEEE 118-bus system are presented and discussed, demonstrating the benefits of this dynamic TNEP approach with respect to classical methods.Comment: 10 pages, 2 figures. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.2629266, IEEE Transactions on Power Systems 201