Structural analysis of complex ecological economic optimal control problems

This thesis demonstrates the importance and effectiveness of methods of bifurcation theory applied to studying non-convex optimal control problems. It opens up a new methodological approach to investigation of parameterized economic models. While standard analytical methods are not efficient and sometimes impossible to apply to non-convex problems, the numerical geometrical methods developed in the thesis allow to solve and analyze such problems quickly.

[1]  Gustav Feichtinger,et al.  Stochastic Skiba Sets: An Example from Models of Illicit Drug Consumption , 2009, LSSC.

[2]  Colin W. Clark,et al.  Mathematical Bioeconomics: The Optimal Management of Renewable Resources. , 1993 .

[3]  F. Wagener,et al.  Managing the environment and the economy in the presence of hysteresis and irreversibility , 2008 .

[4]  J. Caulkins,et al.  Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption, and Terror , 2008 .

[5]  S. Gupta,et al.  The Study of the Impact of Early Life Conditions on Later Life Events: A look across the individual's life course , 2010 .

[6]  J. Hoop Keeping Kids in School. Cash Transfers and Selective Education in Malawi , 2011 .

[7]  Anastasios Xepapadeas,et al.  The Economics of Shallow Lakes , 2000 .

[8]  E. Jongen Modelling the Impact of Labour Market Policies in the Netherlands , 2010 .

[9]  W. Fleming Stochastic Control for Small Noise Intensities , 1971 .

[10]  Richard F. Hartl,et al.  Why Politics Makes Strange Bedfellows: Dynamic Model with DNS Curves , 2001 .

[11]  J. van der Wal,et al.  Dynamic Delay Management at Railways - a Semi-Markovian Decision Approach , 2003 .

[12]  Pim Heijnen,et al.  Environmental Policy and the Macroeconomy Under Shallow-Lake Dynamics , 2009, SSRN Electronic Journal.

[13]  J. Sol Incentives and Social Relations in the Workplace , 2006 .

[14]  Anne-Sophie Crépin,et al.  Using Fast and Slow Processes to Manage Resources with Thresholds , 2007 .

[15]  Jonathan P. Caulkins,et al.  Optimal Dynamic Allocation of Treatment and Enforcement in Illicit Drug Control , 2001, Oper. Res..

[16]  D. Grass Numerical computation of the optimal vector field in a fishery model , 2010 .

[17]  Vladimir Igorevich Arnold,et al.  Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[18]  Florian Wagener,et al.  Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict , 2009, Comput. Manag. Sci..

[19]  E. Demirel Economic Models for Inland Navigation in the Context of Climate Change , 2005 .

[20]  Jonathan P. Caulkins,et al.  Skiba thresholds in a model of controlled migration , 2005 .

[21]  R. Ruth,et al.  Stability of dynamical systems , 1988 .

[22]  Anastasios Xepapadeas,et al.  Feedback Nash equilibria for non-linear differential games in pollution control , 2008 .

[23]  X. Liu Three essays on real estate finance , 2010 .

[24]  Economic development and growth in transition countries , 2010 .

[25]  J. Liu,et al.  Breaking the ice between government and business:: from IT-enabled control procedure redesign to trusted relationship building , 2010 .

[26]  Flavio Toxvaerd,et al.  The Optimal Control of Infectious Diseases Via Prevention and Treatment , 2012 .

[27]  J. Niemczyk Consequences and detection of invalid exogeneity conditions , 2009 .

[28]  Hugo Fort,et al.  Catastrophic shifts in ecosystems: spatial early warnings and management procedures (Inspired in the physics of phase transitions) , 2010 .

[29]  E. Wagenmakers,et al.  Transformation invariant stochastic catastrophe theory , 2005 .

[30]  A. Al Ibrahim,et al.  Dynamic delay management at railways: a Semi-Markovian Decision approach , 2010 .

[31]  Chris van Klaveren The Intra-household Allocation of Time , 2009 .

[32]  E. G. Puigarnau Labour markets, commuting and company cars , 2011 .

[33]  B. Dijk Essays on Finite Mixture Models , 2004 .

[34]  Florian Wagener,et al.  Skiba points and heteroclinic bifurcations, with applications to the shallow lake system , 2003 .

[35]  Richard F. Hartl,et al.  Keeping up with the technology pace: A DNS-curve and a limit cycle in a technology investment decision problem , 2005 .

[36]  A. Skiba,et al.  Optimal Growth with a Convex-Concave Production Function , 1978 .

[37]  M. Holmes Introduction to Perturbation Methods , 1995 .

[38]  K. Lee Filtering Non-Linear State Space Models : Methods and Economic Applications , 2010 .

[39]  Peter M. Kort,et al.  A DNS-curve in a two-state capital accumulation model: A numerical analysis , 2003 .

[40]  Academisch Proefschrift,et al.  Adaptation to Climate Change in Inland Waterway Transport , 2009 .

[41]  K. Judd Numerical methods in economics , 1998 .

[42]  Floris Takens,et al.  Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors , 1993 .

[43]  The Economics of Shallow Lakes , 2003 .

[44]  F. Verhulst Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics , 2010 .

[45]  Kazuo Nishimura,et al.  A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function , 1983 .

[46]  H. J. Kushner,et al.  Optimal Discounted Stochastic Control for Diffusion Processes , 1967 .

[47]  P. Souganidis,et al.  Asymptotic Series and the Methods of Vanishing Viscosity , 1985 .

[48]  F. Wagener,et al.  A bifurcation theory for a class of discrete time Markovian stochastic systems , 2008 .

[49]  Stuart McDonald,et al.  Rent Seeking Behavior and Optimal Taxation of Pollution in Shallow Lakes , 2007 .

[50]  W. Kyner Invariant Manifolds , 1961 .

[51]  V. Boltyanskii Sufficient Conditions for Optimality and the Justification of the Dynamic Programming Method , 1966 .

[52]  K.M.C. Lee Psychological Aspects of the Disposition Effect: An Experimental Investigation , 2011 .

[53]  John Stachurski Stochastic Growth with Increasing Returns: Stability and Path Dependence , 2003 .

[54]  Gabriella Budai-Balke Operations Research Models for Scheduling Railway Infrastructure Maintenance , 2002 .

[55]  C. Main From Mind to Market , 2010 .

[56]  F. Wagener Skiba Points for Small Discount Rates , 2006 .

[57]  Alexei Parakhonyak Essays on Consumer Search Dynamic Competition and Regulation , 2005 .

[58]  M. Ochea Essays on nonlinear evolutionary game dynamics , 2010 .

[59]  S. Salo,et al.  Nonconvexities in Optimal Pollution Accumulation , 1996 .

[60]  Vincent A. C. van den Berg Congestion pricing with heterogeneous travellers , 2007 .

[61]  Sabine C P J Go Marine Insurance in the Netherlands 1600-1870: A Comparative Institutional Approach , 2009 .

[62]  Jonathan P. Caulkins,et al.  Keeping Options Open: an Optimal Control Model with Trajectories That Reach a DNSS Point in Positive Time , 2010, SIAM J. Control. Optim..

[63]  Genesis of indifference thresholds and infinitely many indifference points in discrete time infinite horizon optimisation problems , 2009 .

[64]  G. Thompson,et al.  Optimal Control Theory: Applications to Management Science and Economics , 2000 .

[65]  A. Dubovik Economic Dances for Two (and Three) , 2010 .

[66]  H. Dawid,et al.  On the efficiency-effects of private (dis-)trust in the government , 2005 .

[67]  Marten Scheffer,et al.  Critical Transitions in Nature and Society , 2009 .

[68]  Academisch Proefschrift,et al.  The Moral Herd: Groups and the Evolution of Altruism and Cooperation , 2011 .

[69]  Suresh P. Sethi,et al.  Optimal advertising policy with the contagion model , 1979 .

[70]  D. V. Dijk Understanding Socioeconomic Differences in Health An Economic Approach , 2010 .

[71]  William A. Brock,et al.  Managing Systems with Non-convex Positive Feedback , 2003 .

[72]  G. Feichtinger,et al.  Skiba Thresholds in Optimal Control of Illicit Drug Use , 2002 .

[73]  J. Caulkins,et al.  Bifurcating DNS Thresholds in a Model of Organizational Bridge Building , 2007 .

[74]  Florian Wagener,et al.  Bifurcations of optimal vector fields in the shallow lake model , 2010 .

[75]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[76]  E. C. Zeeman,et al.  Stability of dynamical systems , 1988 .

[77]  van Hans Kippersluis,et al.  Understanding Socioeconomic Differences in Health An Economic Approach , 2010 .

[78]  Essays on top management and corporate behavior , 2010 .

[79]  M. Reinders Managing consumer resistance to innovations , 2010 .

[80]  Academisch Proefschrift,et al.  Credit Risk and State Space Methods , 2011 .

[81]  Florian Wagener,et al.  From Mind to Market: A Global, Dynamic Analysis of R&D , 2011 .

[82]  W. Dechert,et al.  The stochastic lake game: A numerical solution , 2006 .

[83]  Suresh P. Sethi,et al.  Nearest feasible paths in optimal control problems: Theory, examples, and counterexamples , 1977 .

[84]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[85]  A.I.W. Hindrayanto Periodic Seasonal Time Series Models with applications to U.S. macroeconomic data , 2004 .