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[CT169]

Session Time & Room : 4C (Aug.24, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.
Classification : 90C40, 91G10, Robust Finance
Format : Talk at Waseda University
Author(s) :
- Julian Sester (National University of Singapore)
- Ariel Neufeld (Nanyang Technological University)
- Mario Šikić (University of Zurch)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : In radiotherapy treatment, is it possible to vary the radiation intensity, achieving a dose distribution with superior compliance. An individualized treatment plan comprises information on how the dose is distributed within a patient. The dose distribution problem translates into optimizing the total radiation dose applied to the patient. Fuzzy optimization is used to deal with inaccurate prescription. Interior point methods are applied to determine optimal solutions with less dose distribution in critical organs.
Classification : 90C51, 90C05, 90C70
Format : Talk at Waseda University
Author(s) :
- Aurelio Oliveira (University of Campinas)
- Nicole Cassimiro (University of Campinas)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : At the heart of all quasi-Newton methods is an update rule that enables us to gradually improve the Hessian approximation using the already available gradient evaluations. Theoretical results show that the global performance of optimization algorithms can be improved with higher-order derivatives. This motivates an investigation of generalizations of quasi-Newton update rules to obtain for example third derivatives (which are tensors) from Hessian evaluations. Our generalization is based on the observation that quasi-Newton updates are least-change updates satisfying the secant equation, with different methods using different norms to measure the size of the change. We present a full characterization for least-change updates in weighted Frobenius norms (satisfying an analogue of the secant equation) for derivatives of arbitrary order. Moreover, we establish convergence of the approximations to the true derivative under standard assumptions and explore the quality of the generated approximations in numerical experiments.
Classification : 90C59, 90C53
Format : Talk at Waseda University
Author(s) :
- Karl Welzel (University of Oxford)
- Raphael Hauser (University of Oxford)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @A207
Type : Contributed Talk
Abstract : Most real-world optimization problems have a hierarchical structure. In mathematical optimization, hierarchical optimization problems are often known as multilevel programming problems. A particular case of multilevel problems with just two decision-makers is called a bilevel programming problem. In the formal framework of bilevel programming problems, two decision-makers are involved, a leader and a follower, at two different levels, each striving to minimize their objective functions while constrained by several interconnected constraints.
Classification : 90C46, 49J52, 90C99
Author(s) :
- Shivani Saini (Thapar Institute of Engineering and Technology, Patiala, Punjab)