Springer Proceedings in Mathematics & Statistics Fred Espen Benth Giulia Di Nunno Editors Stochastics of Environmental and Financial Economics Centre of Advanced Study, Oslo, Norway, 2014–2015 Springer Proceedings in Mathematics & Statistics Volume 138 Springer Proceedings in Mathematics & Statistics This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including operation research and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today. More information about this series at http://www.springer.com/series/10533 Fred Espen Benth Giulia Di Nunno (cid:129) Editors Stochastics of Environmental and Financial Economics Centre of Advanced Study, Oslo, Norway, – 2014 2015 Editors FredEspen Benth Giulia DiNunno Department ofMathematics Department ofMathematics University of Oslo University of Oslo Oslo Oslo Norway Norway ISSN 2194-1009 ISSN 2194-1017 (electronic) SpringerProceedings in Mathematics& Statistics ISBN978-3-319-23424-3 ISBN978-3-319-23425-0 (eBook) DOI 10.1007/978-3-319-23425-0 LibraryofCongressControlNumber:2015950032 Mathematics Subject Classification: 93E20, 91G80, 91G10, 91G20, 60H30, 60G07, 35R60, 49L25, 91B76 SpringerChamHeidelbergNewYorkDordrechtLondon © The Editor(s) (if applicable) and the Author(s) 2016. The book is published with open access at SpringerLink.com. Open Access This book is distributed under the terms of the Creative Commons Attribution NoncommercialLicense,whichpermitsanynoncommercialuse,distribution,andreproductioninany medium,providedtheoriginalauthor(s)andsourcearecredited. All commercial rights are reserved by the Publisher, whether the whole or part of the material is concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformationstorageand retrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknown orhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia (www.springer.com) Preface Norwayisacountryrichonnaturalresources.Wind,rainandsnowprovideuswith a huge resource for clean energy production, while oil and gas have contributed significantly, since the early 1970s, to the country’s economic wealth. Nowadays theincomefromoilandgasexploitationisinvestedintheworld’sfinancialmarkets to ensure the welfare offuture generations. With the rising global concerns about climate, using renewable resources for power generation has become more and more important. Bad management of these resources will be a waste that is a negligence to avoid given the right tools. This formed the background and motivation for the research group Stochastics for Environmental and Financial Economics (SEFE) at the Centre of Advanced Studies (CAS) in Oslo, Norway. During the academic year 2014–2015, SEFE hosted a number of distinguished professors from universities in Belgium, France, Germany,Italy,Spain,UKandNorway.ThescientificpurposeoftheSEFEcentre was to focus on the analysis and management of risk in the environmental and financial economics. New mathematical models for describing the uncertain dynamics in time and space of weather factors like wind and temperature were studied, along with sophisticated theories for risk management in energy, com- modity and more conventional financial markets. In September 2014 the research group organized a major international confer- ence on the topics of SEFE, with more than 60 participants and a programme running over five days. The present volume reflects some of the scientific devel- opments achieved by CAS fellows and invited speakers at this conference. All the 14 chapters arestand-alone, peer-reviewed research papers. The volume is divided into two parts; the first part consists of papers devoted to fundamental aspects of stochasticanalysis,whereasinthesecondpartthefocusisonparticularapplications to environmental and financial economics. v vi Preface WethankCASforitsgeneroussupportandhospitalityduringtheacademicyear we organized our SEFE research group. We enjoyed the excellent infrastructure CAS offered for doing research. Oslo, Norway Fred Espen Benth June 2015 Giulia Di Nunno Contents Part I Foundations Some Recent Developments in Ambit Stochastics . . . . . . . . . . . . . . . . 3 Ole E. Barndorff-Nielsen, Emil Hedevang, Jürgen Schmiegel and Benedykt Szozda Functional and Banach Space Stochastic Calculi: Path-Dependent Kolmogorov Equations Associated with the Frame of a Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . 27 Andrea Cosso and Francesco Russo Nonlinear Young Integrals via Fractional Calculus. . . . . . . . . . . . . . . 81 Yaozhong Hu and Khoa N. Lê A Weak Limit Theorem for Numerical Approximation of Brownian Semi-stationary Processes. . . . . . . . . . . . . . . . . . . . . . . . 101 Mark Podolskij and Nopporn Thamrongrat Non-elliptic SPDEs and Ambit Fields: Existence of Densities. . . . . . . . 121 Marta Sanz-Solé and André Süß Part II Applications Dynamic Risk Measures and Path-Dependent Second Order PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Jocelyne Bion-Nadal Pricing CoCos with a Market Trigger. . . . . . . . . . . . . . . . . . . . . . . . . 179 José Manuel Corcuera and Arturo Valdivia vii viii Contents Quantification of Model Risk in Quadratic Hedging in Finance. . . . . . 211 Catherine Daveloose, Asma Khedher and Michèle Vanmaele Risk-Sensitive Mean-Field Type Control Under Partial Observation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Boualem Djehiche and Hamidou Tembine Risk Aversion in Modeling of Cap-and-Trade Mechanism and Optimal Design of Emission Markets. . . . . . . . . . . . . . . . . . . . . . 265 Paolo Falbo and Juri Hinz Exponential Ergodicity of the Jump-Diffusion CIR Process. . . . . . . . . 285 Peng Jin, Barbara Rüdiger and Chiraz Trabelsi Optimal Control of Predictive Mean-Field Equations and Applications to Finance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Bernt Øksendal and Agnès Sulem Modelling the Impact of Wind Power Production on Electricity Prices by Regime-Switching Lévy Semistationary Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Almut E.D. Veraart Pricing Options on EU ETS Certificates with a Time-Varying Market Price of Risk Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 Ya Wen and Rüdiger Kiesel Part I Foundations