- Date: May 4, 2011
- Place: IWR, Heidelberg, INF 368, Room 432
- Target group: guests, MathComp doctoral and master students.

The workshop will be organized by Tony Huschto and Sebastian Sager from the MathOpt research group.

Holger Diedam received his diploma in mathematics in 2009 at the University of Heidelberg, spending research periods at the Ho Chi Minh City University of Technology, Vietnam and the INRIA Grenoble, France.

He is currently holding a Doctoral stipend from the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences. His research interests include nonlinear mixed-integer dynamic optimization, global dynamic optimization and automatic model generation with applications in economics.

We present a deterministic, nonlinear model of petrochemical products and processes. In this model, the price is determined as a result of an optimization. Due to the lack of accumulated data on the price and demand correlation, a demand-price function is estimated on the data of previous years taking into account the forecasts of several global development indicators.

Furthermore, possible applications of such a macroeconomic model for industrial partners are discussed and possible interesting scenarios, together with first simulation results of a small submodel, are presented. The topic is currently work in progress and any discussion is appreciated.

Dieter Grass is a research assistant at the research unit "Operations Research and Control Systems" (ORCOS, TU Vienna). His scientific interests are mainly optimal control theory, bifurcation, numerics, and applications.

**Education**- 2004: PhD in Mathematics, TU Vienna
- 1996: Diplom in Mathematics, University of Vienna

**Academic Appointments**- 2010 - present: Research assistant at ORCOS
- 2009-10: Research Assistant for the project Arctic Tipping Points (ATP) at the Beijer Institute of Ecological Economics at the Royal Swedish Academy of Sciences
- 2002-09: Research assistant at ORCOS
- 1997-2002: Research work at the Institute for Theoretical Biology (University of Vienna), and at the Institute for Educational Science (Univeristy of Innsbruck)

Optimal control problems in economy are often considered over an infinite time horizon. This raises the question on how to formulate the end condition at infinite, since the transversality condition does not provide "useful" numerical information. In this talk I present the necessary numerical basics to reformulate the condition at infinite as a boundary value problem. Within this approach we can even handle constrained problems taking care of the switches between arcs of active and inactive constraints.

Combined with a continuation algorithm this is an efficient approach to follow, among other things, bifurcations of the optimal dynamics and calculate indifference surfaces, where multiple optimal solutions exist.

This is already implemented in a MATLAB package (OCMat), and will further be extended and enhanced. This talk is a shortened version of a seminar, held at the Technical University of Vienna. The complete Seminar notes together with a version of the package can be downloaded from: http://orcos.tuwien.ac.at/research/ocmat_software

Tony Huschto is a PhD student at the University of Heidelberg. His research interests are in stochastic differential equations and optimal control, as well as their applications to economics.

**Education**- 2009: Diploma in Mathematics, BTU Cottbus
- 2008: M.Sc. in Financial Mathematics, Högskolan Halmstad, Sweden

In periods of recession particular pricing strategies for conspicuous consumption products are required. To derive such strategies, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account.

We propose a structure-exploiting direct method for optimal control to solve this challenging problem, discretizing uncertainties in the model formulation by using scenario trees and targeting the control delays by introducing slack control function. Numerical results illustrate the validity of our approach and the impact of uncertainties and delay effects on optimal economic strategies.

Additionally, we will present how different approaches of robust optimization affect those optimal pricing strategies and give an outlook on further ideas to be applied.

Peter Kort was born in Zierikzee, the Netherlands in 1961. He received a M.Sc degree in 1984 from the Erasmus University Rotterdam and a Ph.D. from Tilburg University in 1988. In 1991 he became research fellow of the Royal Netherlands Academy of Arts and Sciences. Currently he is full professor in Dynamic Optimization in Economics and Operations Research at Tilburg University and Guest Professor at the University of Antwerp. His main research areas are applied optimal control, dynamics of the firm, real options theory, and strategic industrial organization, in which he published about 85 papers in refereed international journals.

The paper considers two firms that both invest in capital goods to produce an established product. Now, one of the firms has the option to introduce a strongly differentiated product thereby opening a new submarket. The research questions we consider are the following. First, how does the option to invest in the new market affect the capacity dynamics of both firms? Second, what is the value of the innovation option for the innovating firm. Third, how is the non-innovating firm affected by the innovation (option) of its competitor?

**Education**- 1977: Habilitation, University of Würzburg
- 1972: PhD in Applied Mathematics, University of Cologne

**Academic Appointments**- 1977: Professor of Applied Mathematics at the University of Münster, retired since 10/2010.
- 1973/74: Postdoctoral fellow at the University of British Columbia

The talk addresses optimal control problems with state delays and state constraints. A Pontryagin type Minimum Principle is obtained by augmenting the delayed control problem to an non-delayed control problem of higher dimension. We briefly discuss discretization and nonlinear programming problems for resolving the delayed control problem. The focus in this talk is on two economic applications: (1) optimal control of a model of climate change with state constraints on temperature and carbon dioxide emissions, (2) a complex bio-economic model: optimal control of the immune system facing a virus attack. This is joint work with M. Bruns, J.J. Preuß and W. Semmler.

**Education**- 1992: Habilitation at Leipzig University
- 1979 - 1982: PhD student at Leipzig University, PhD 1983
- 1973 - 1979: Study of Mathematics in Leipzig

**Academic Appointments**- 1993 - present: Chair of Optimization at Technical University Cottbus
- 1982 - 1993: Scientific staff member Mathematical Institute, Leipzig University

Up to now, it was not possible to prove a Pontryagin type maximum principle as separation theorem in Banach spaces, including adequate transversality conditions for infinite horizon optimal control problems in general.

Several examples are discussed to see the difficulties. For a special example we show, that for the adjoints (λ_{1}=1, ψ) continuity of φ is violated.

Andrea Seidl received a masters degree in "economics and computer science" in 2005 and a PhD degree in 2009 both from the Vienna University of Technology. Currently she works as a postdoctoral research assistant at the Institute for Mathematical Methods in Economics at the Vienna University of Technology. Her research interests include optimal control and its applications, in particular multi-stage models.

Software can be distributed closed source (proprietary) or open source (developed collaboratively). Previous papers have considered firm's option to release a software under a closed or open source license as a simple once and for all time binary choice. We generalize this to a multi-stage optimal control model that allows for the possibility of keeping software proprietary for some optimally determined finite time period before making it open source. We will also consider how the additional option to make open source software closed source at some optimally determined time and restrictions on the number of switches affect the optimal solution.

**Education**- 2010: PhD in Mathematics, BTU Cottbus
- 1997 - 2004: Study of Mathematics in Leipzig

**Academic Appointments**- 2010 - present: Leader of the Junior Research Group "Hybride Systeme" in Cottbus
- 2005 - 2010: Scientific staff member in Cottbus

Based on the model of Bloom et al. "A Theory of Retirement" (2007) we construct a life-cycle model with an additional control parameter for education.

In our model education improves the prospective salary class. We show that in the duration of education the total proportion the worker is spending in labor and education increases. At the same time we observe a renouncement in the living standard.

Ralph Winkler is an Assistant Professor at the Department of Economics and the Oeschger Centre for Climate Change Research at the University of Bern. His research interests are in the theory of economic growth, climate change and environmental policy.

**Education**- 06/2000-07/2003: Doctoral Dissertation at the Interdisciplinary Institute for Environmental Economics, University of Heidelberg
- 04/1996-12/2000: Graduate studies in Economics, University of Heidelberg
- 11/1993-02/1999: Graduate studies in Physics, TUM, Munich, and University of Heidelberg

**Academic Appointments**- since 08/2009: Assistant Professor at the University of Bern
- 06/2006-07/2009: Post-Doctoral Research Fellow at the Center of Economic Research at ETH Zurich (CER-ETH)
- 02/2004-02/2006: Post-Doctoral Research Fellow at the School of Politics, International Relations and the Environmnet (SPIRE), Keele University
- 07/2003-12/2003: Post-Doctoral Research Fellow at the Interdisciplinary Institute for Environmental Economics, University of Heidelberg
- 10/2001-06/2003: Research and Teaching Assistant at the Department of Economics, University of Heidelberg

We study the welfare-theoretic consequences of diverging social and private time-preference rates and time-to-build for the transition to a low-carbon energy industry. We show that time-to-build, a prevalent characteristic of capital accumulation in the energy sector, amplifies the distortion induced by the split discount rates. Thus, these two characteristics create in a mutually reinforcing way less favorable circumstances for the introduction of new clean energy technologies as compared to the social optimum, even if welfare losses from emissions are internalized. We discuss resulting policy implications with particular emphasis on the energy sector.

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Time | Wednesday, May 4th, 2011 |
---|---|

09h00-09h15 | Welcome |

09h15-10h00 | Peter Kort: Dynamic Strategic Interaction Between an Innovating and a Non-innovating Incumbent |

10h00-10h45 | Dieter Grass: Numerical method for infinite time horizon optimal control problems |

10h45-11h15 | Coffee break |

11h15-12h00 | Helmut Maurer: Economic applications of retarded optimal control problems with state constraints |

12h00-12h45 | Holger Diedam: A Deterministic Approach to Price Forecasting and Scenario Simulation in the Petrochemical Industry |

12h45-14h15 | Lunch |

14h15-15h00 | Sabine Pickenhain: Maximum principle - core relations and transversality conditions for infinite horizon optimal control problems - the examples of Halkin |

15h00-15h45 | Andrea Seidl: When to Make Proprietary Software Open Source? |

15h45-16h30 | Tony Huschto: Numerical Solution of a Conspicuous Consumption Model |

16h30-17h00 | Coffee break |

17h00-17h45 | Ralph Winkler: Distorted Time Preferences and Time-to-Build in the Transition to a Low-Carbon Energy Industry |

17h45-18h30 | Nico Tauchnitz: A Retirement Model with Control Parameters for Labor, Savings, Credits and Education |

18h30- | Workshop Dinner |

The slides of all presentations can be found at this restricted page.

Last Modification: 2016-05-12 - Contact Person: Sebastian Sager - Impressum