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Applications of Stochastic Optimal Control to Economics and Finance A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Federico, Salvatore (Ed.); Ferrari, Giorgio (Ed.); Regis, Luca (Ed.) Book — Published Version Applications of stochastic optimal control to economics and finance Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Federico, Salvatore (Ed.); Ferrari, Giorgio (Ed.); Regis, Luca (Ed.) (2020) : Applications of stochastic optimal control to economics and finance, ISBN 978-3-03936-059-8, MDPI, Basel, http://dx.doi.org/10.3390/books978-3-03936-059-8 This Version is available at: http://hdl.handle.net/10419/230540 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ www.econstor.eu Applications of Stochastic Optimal Control to Economics and Finance Applications of Stochastic • Salvatore Federico, Giorgio Ferrari and Luca Regis Optimal Control to Economics and Finance Edited by Salvatore Federico, Giorgio Ferrari and Luca Regis Printed Edition of the Special Issue Published in Risks www.mdpi.com/journal/risks Applications of Stochastic Optimal Control to Economics and Finance Applications of Stochastic Optimal Control to Economics and Finance Special Issue Editors Salvatore Federico Giorgio Ferrari Luca Regis MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Special Issue Editors Salvatore Federico Giorgio Ferrari Luca Regis University of Siena Bielefeld University University of Torino Italy Germany Italy Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Risks (ISSN 2227-9091) (available at: https://www.mdpi.com/journal/risks/special issues/Stochastic Optimal Control). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03936-058-1 (Hbk) ISBN 978-3-03936-059-8 (PDF) c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editors ..................................... vii Preface to ”Applications of Stochastic Optimal Control to Economics and Finance” ...... ix Jason S. Anquandah and Leonid V. Bogachev Optimal Stopping and Utility in a Simple Model of Unemployment Insurance Reprinted from: Risks 2019, 7, 94, doi:10.3390/risks7030094 ...................... 1 Francesco Rotondi American Options on High Dividend Securities: A Numerical Investigation Reprinted from: Risks 2019, 7, 59, doi:10.3390/risks7020059 ...................... 43 Matteo Brachetta and Claudia Ceci Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models Reprinted from: Risks 2019, 7, 48, doi:10.3390/risks7020048 ...................... 63 John Moriarty and Jan Palczewski Imbalance Market Real Options and the Valuation of Storage in Future Energy Systems Reprinted from: Risks 2019, 7, 39, doi:10.3390/risks7020039 ...................... 87 Zbigniew Palmowski, Łukasz Stettner and Anna Sulima Optimal Portfolio Selection in an Ito–Markovˆ Additive Market Reprinted from: Risks 2019, 7, 34, doi:10.3390/risks7010034 ......................117 Carmine De Franco, Johann Nicolle and Huyˆen Pham Dealing with Drift Uncertainty: A Bayesian Learning Approach Reprinted from: Risks 2019, 7, 5, doi:10.3390/risks7010005 .......................149 Abel Cadenillas and Ricardo Huam´an-Aguilar On the Failure to Reach the Optimal Government Debt Ceiling Reprinted from: Risks 2018, 6, 138, doi:10.3390/risks6040138 .....................167 v About the Special Issue Editors Salvatore Federico is an Associate Professor of mathematics for economics and finance at the University of Siena. He holds a PhD from Scuola Normale Superiore in the field of financial mathematics. Giorgio Ferrari is an Associate Professor of mathematical finance at the Center for Mathematical Economics at Bielefeld University. He holds a PhD in mathematics for economic-financial applications from the University of Rome “La Sapienza”. His main research interests are the theory and application of singular stochastic control, optimal stopping, and stochastic games. Luca Regis is an Associate Professor of mathematics for finance and insurance at the University of Torino, ESOMAS Department. His research interests are in the interplay between financial and actuarial mathematics, and include corporate finance. vii Preface to “Applications of Stochastic Optimal Control to Economics and Finance” In a world dominated by uncertainty, the modeling and understanding of the optimal behavior of agents are of the utmost importance. Many problems in economics, finance, and actuarial science naturally require decision-makers to undertake choices in stochastic environments. Examples include optimal individual consumption and retirement choices, optimal management of portfolios and risk, hedging, optimal timing issues in pricing American options, or in investment decisions. Stochastic control theory provides the methods and results to tackle all such problems. This book collects the papers published in the 2019 Special Issue of Risks “Applications of Stochastic Optimal Control to Economics and Finance” and contains 7 peer-reviewed papers dealing with stochastic control models motivated by important questions in Economics and Finance. Each model is mathematically rigorously funded and treated, and numerical methods are also possibly employed to derive the optimal solution. The topics of the book’s chapters range from optimal public debt management, to optimal reinsurance, real options in energy markets, and optimal portfolio choice in partial and complete information setting, just to mention a few. From a mathematical point of view, techniques and arguments from dynamic programming theory, filtering theory, optimal stopping, one-dimensional diffusions, and multi-dimensional jump processes are used. The paper by Anquandah and Bogachev deals with unemployment insurance and proposes a simple model of optimal agent entrance in a scheme. The paper analyzes individual decisions regarding optimal entry time, the dependence of the optimal solution on macroeconomic variables, and individual preferences. In the second paper of the Special Issue, Rotondi documents a bias that may arise when American options are monetarily valued using the traditional least square method. The estimates on which this method is based utilize a regression run of the in-the-money paths of the Monte Carlo simulation. Therefore, large biases may occur if, for instance, the option is far out of the money. The paper proposes two approaches that completely overcome this problem and evaluates their performance, using the standard least square method. In the third paper, Ceci and Brachetta study optimal excess-of-loss reinsurance problems when both the intensity of the claims’ arrival and the claims’ size are influenced by an exogenous stochastic factor. The model allows for stochastic risk premia, which takes into account risk fluctuations. Using stochastic control theory, based on the Hamilton–Jacobi– Bellman equation, the authors analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of terminal wealth. In the fourth paper, Moriarty and Palczewski study a real option problem arising in the context of energy markets. They assess the real option value of an arrangement under which an autonomous energy-limited storage unit sells incremental balancing reserve. The problem is set as a perpetual American swing put option with random refraction times. In the fifth paper, Palmowski, Stettner, and Sulima study a portfolio selection problem in a continuous-time Itô–Markov additive market, where the prices of financial assets are described by the Markov additive processes that combines Lévy processes and regime- switching models. The model takes into account two sources of risk: the jump-diffusion risk and the regime-switching risk. The
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