4 Presentations

• 
  08:30 AM - 09:00 AM

  Contraction approach to optimization problems

  • Leif Kristoffer Sandal, presenter, NHH
  • Sturla K Kvamsdal, NHH
  • José M Maroto, Universidad Complutense, De Madrid
  • Manuel Morán, Universidad Complutense, Madrid

  Consider an infinite horizon, multi-dimensional optimization problem with arbitrary but finite periodicity in discrete time. The problem can be posed as a set of coupled equations. We show that it is a special case of a more general class of contraction problems which has a unique solution obtained by an iterative process. Special cases include the classical Bellman problem and its stochastic problem formulations. Thus, we view our approach as an extension of the Bellman problem to the special case of non-autonomy that periodicity represents, and we thereby pave the way for consistent and rigorous treatment of, for example, seasonality in discrete, dynamic optimization and certain types of dynamic games. We demonstrate our results with two examples; a case with a simple periodic variation in the objective function and a simple dynamic game.

• 
  09:00 AM - 09:30 AM

  Insurance and forest rotation decisions under storm risk

  • Patrice Loisel, INRA
  • Marielle Brunette, INRA
  • Stéphane Couture, presenter, INRA

  In this paper, we analyze the impact of the forest owner's insurance decision on forest management under storm risk. First, we introduce insurance decision into the Faustmann optimal rotation model under risk, and we derive analytical expressions for the optimal cutting age. Second, we integrate the forest owner's risk preferences into the model. Third, the definition of the insurance terms is principally based on the level of the expected loss. As the loss is endogenous to the forest management, we propose to model the microeconomic behavior of the insurer in order to precisely define the components of the insurance contract.

• 
  09:30 AM - 10:00 AM

  Industry consolidation under spatial-dynamic externalities

  • Felix Morency-Lavoie, presenter, Norwegian School of Economics
  • Linda Nøstbakken, Norwegian School of Economics
  • Joshua Abbott, Arizona State University

  This paper investigates how spatial externalities can drive firms’ consolidation. Theory suggests that intra-industry spatial externalities create incentives for affected producers to take control of polluting neighboring assets through mergers and acquisitions. We develop a model with asymmetric spatial cross-contamination among plants to test empirically if consolidation in Norwegian salmon aquaculture was partly motivated by internalization of parasitic externalities. Our unique plant-level dataset includes detailed information on production, environmental quality, and financial indicators. We find evidence that firms make acquisitions to mitigate contamination risk. Consequently, the presence of an important externality may have understudied implications for an industry’s structure.

• 
  10:00 AM - 10:30 AM

  A physico-economic model of orbital management

  • Sébastien Rouillon, presenter, GREThA - University of Bordeaux

  We solve a stylized physico-economic model of orbital environment and space activity, in order to analyse the externality caused by the accumulation of space debris. In line with Gordon (1954) and Schaeffer (1957), we focus on the long term equilibrium of the orbit, induced by a constant rate of launching forever. We show that if, in the long run, the risk of satellite destruction by collision is increasing and convex with the launch rate and becomes arbitrarily large for finite values of the latter, then the curve representing the long term expected number of functioning satellites, as a function of the launch rate, has a reversed-U shape. Classically, we then define and compare typical ways of managing the orbital environment (maximum carrying capacity, open-access, social optimum). The maximum carrying capacity is defined as the maximum expected number of satellites that the orbit can sustain in the long run. The physico-economic equilibrium launch rate, that would presumably emerge under conditions of open-access to the orbit, is defined as the rate of launching such that the space sector makes no profit. Finally, the socially optimal rate of launching is the one that maximizes the present value profit of the space sector per launching campaign.