This paper presents a general framework for studying diverse beliefs in dynamic economies. Within this general framework, the characterization of a central-planner general equilbrium turns out to be very easy to derive, and leads to a range of interesting applications. We show how for an economy with log investors holding diverse beliefs, rational overconfidence is to be expected; volume-of-trade effects are effectively modelled; the Keynesian 'beauty contest' can be modelled and analysed; and bubbles and crashes arise naturally. We remark that models where agents receive private information can formally be considered as models of diverse beliefs. * Wilberforce Road, Cambridge CB3 0WB, UK (phone = +44 1223 337969 , email = A.A.Brown@statslab.cam.ac.uk) † Wilberforce Road, Cambridge CB3 0WB, UK (phone = +44 1223 766806, email = L.C.G.Rogers@statslab.cam.ac.uk) We thank seminar participants at the Cambridge-Wharton meeting, June 2009, particularly our discussant, Frank Diebold.

For an unmanned aerial vehicle (UAV) carrying out a maritime radar surveillance mission, there is a tradeoff between maximizing information obtained from the search area and minimizing fuel consumption. This article presents an approach for the optimization of a UAV's trajectory for maritime radar wide area persistent surveillance to simultaneously minimize fuel consumption, maximize mean probability of detection, and minimize mean revisit time. Quintic polynomials are used to generate UAV trajectories due to their ability to provide complete and complex solutions while requiring few inputs. Furthermore, the UAV dynamics and surveillance mission requirements are used to ensure that a trajectory is realistic and mission compatible. A wide area search radar model is used within this article in conjunction with a discretized grid in order to determine the search area's mean probability of detection and mean revisit time. The trajectory generation method is then used in conjunction with a multiobjective particle swarm optimization algorithm to obtain a global optimum in terms of path, airspeed (and thus time), and altitude. The performance of the approach is then tested over two common maritime surveillance scenarios and compared to an industry recommended baseline.

This note will extend the research presented in Brown & Rogers (2009) to the case of CRRA agents. We consider the model outlined in that paper in which agents had diverse beliefs about the dividends produced by a risky asset. We now assume that the agents all have CRRA utility, with some integer coefficient of relative risk aversion. This is a generalisation of Brown & Rogers (2009) which considered logarithmic agents. We derive expressions for the state price density, riskless rate, stock price and wealths of the agents. This sheds light on the effects of risk aversion in an equilibrium with diverse beliefs. * Wilberforce Road, Cambridge CB3 0WB, UK (phone = +44 1223 337969 , email = A. A.Brown@statslab.cam.ac.uk)

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