Optimal Financial Decision Making Under Uncertainty
We use a fairly general framework to analyze a rich variety of financial optimization models presented in the literature, with emphasis on contributions included in this volume and a related special issue of OR Spectrum. We do not aim at providing readers
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Optimal Financial Decision Making Under Uncertainty Giorgio Consigli, Daniel Kuhn, and Paolo Brandimarte
Abstract We use a fairly general framework to analyze a rich variety of financial optimization models presented in the literature, with emphasis on contributions included in this volume and a related special issue of OR Spectrum. We do not aim at providing readers with an exhaustive survey, rather we focus on a limited but significant set of modeling and methodological issues. The framework is based on a benchmark discrete-time stochastic control optimization framework, and a benchmark financial problem, asset-liability management, whose generality is considered in this chapter. A wide set of financial problems, ranging from asset allocation to financial engineering problems, is outlined, in terms of objectives, risk models, solution methods, and model users. We pay special attention to the interplay between alternative uncertainty representations and solution methods, which have an impact on the kind of solution which is obtained. Finally, we outline relevant directions for further research and optimization paradigms integration. Keywords Stochastic control • Dynamic programming • Multistage stochastic programming • Robust optimization • Distributionally robust optimization • Decision rules • Asset-liability management • Pension fund management
G. Consigli () Department of Management, Economics and Quantitative Methods, University of Bergamo, Via dei Caniana 2, 24127 Bergamo, Italy e-mail: [email protected] D. Kuhn Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland e-mail: [email protected] P. Brandimarte Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy e-mail: [email protected] © Springer International Publishing Switzerland 2017 G. Consigli et al. (eds.), Optimal Financial Decision Making under Uncertainty, International Series in Operations Research & Management Science 245, DOI 10.1007/978-3-319-41613-7_11
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11.1 The Domain of Financial Optimization Since the seminal work of Markowitz [71], the literature on the application of optimization models to financial decision problems has witnessed an astonishing growth. The contributions presented in this volume and the companion special issue (SI) of OR Spectrum [38] offer a broad picture illustrating a variety of problems and solution approaches that have been the subject of recent research, from both a theoretical and an applied perspective. The main purpose of this chapter is to review the building blocks of recent research on optimization models in finance. We do not aim at giving an exhaustive literature survey, though, and due emphasis is given to contributions to this volume and the SI. The (less ambitious) aim is to reconsider the contributions within a common framework in order to spot research directions and integration opportunities. This should be especially valuable to practitione
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