'This practical review assesses several approaches to solving medium- and large-scale dynamic stochastic general equilibrium (DSGE) models featuring occasionally binding constraints. In such models, global solution methods are not possible because of the curse of dimensionality. This causes the modeller to look elsewhere for methods that can handle the significant non-linearities and non-differentiable functions that inequality constraints represent. The paper discusses methods-including Newton-type solvers under perfect foresight, the piecewise linear algorithm (OccBin), regime-switching models (RISE) and the news shocks approach (DynareOBC) - and compares the results from a simple borrowing constraints model obtained using projection methods, providing example MATLAB code. The study focuses on the news shocks method, which I find produces higher accuracy than other methods and allows the modeller to study multiple equilibria and determinacy issues'--Abstract, page ii.

Modern macroeconomics has been based on the paradigm of the rational individual capable of understanding the complexity of the world. This has created a very shallow theory of the business cycle in which nothing happens in the macroeconomy unless shocks occur from outside. Behavioural Macroeconomics: Theory and Policy uses a different paradigm. It assumes that individual agents experience cognitive limitations preventing them from having rational expectations. Instead these individuals use simple rules of behaviour. Behavioural Macroeconomics introduces rationality by allowing individuals to learn from their mistakes and to switch to the rules that perform better. It introduces the idea of endogenously generated "animals spirits" that drive the business cycle and are in turn influenced by it, and applies this model to shed new light on a number of important issues. It analyses the role of fiscal policy in stabilizing the economy while maintaining debt sustainability; expands the model to include a banking sector and show how banks amplify the booms and busts; and explains how animal spirits help to synchronize the business cycles across countries. The model set out in Behavioural Macroeconomics leads to very different policy implications from the mainstream macroeconomic model. It shows how policymakers have a responsibility to stabilize an otherwise unstable system.

The Oxford Handbook of Computational Economics and Finance provides a survey of both the foundations of and recent advances in the frontiers of analysis and action. It is both historically and interdisciplinarily rich and also tightly connected to the rise of digital society. It begins with the conventional view of computational economics, including recent algorithmic development in computing rational expectations, volatility, and general equilibrium. It then moves from traditional computing in economics and finance to recent developments in natural computing, including applications of nature-inspired intelligence, genetic programming, swarm intelligence, and fuzzy logic. Also examined are recent developments of network and agent-based computing in economics. How these approaches are applied is examined in chapters on such subjects as trading robots and automated markets. The last part deals with the epistemology of simulation in its trinity form with the integration of simulation, computation, and dynamics. Distinctive is the focus on natural computationalism and the examination of the implications of intelligent machines for the future of computational economics and finance. Not merely individual robots, but whole integrated systems are extending their "immigration" to the world of Homo sapiens, or symbiogenesis.

The theoretical and empirical econometric literatures on long memory and regime switching have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related, and we substantiate our claim in several environments, including a simple mixture model, Engle and Lee's (1999) stochastic permanent break model, and Hamilton's (1989) Markov switching model. In particular, we show analytically that stochastic regime switching is easily confused with long memory, even asymptotically, so long as only a small' amount of regime switching occurs, in a sense that we make precise. A Monte Carlo analysis supports the relevance of the theory and produces additional insights.

In this thesis, we address a convex stochastic optimal control problem in mathematical finance, with the goal of minimizing a general quadratic loss function of the wealth at close of trade. We study this problem in the setting of an Ito process market model, in which the underlying filtration to which the market parameters are adapted is the joint filtration of the driving Brownian motion for the market model, together with the filtration of an independent finite-state Markov chain which models occasional changes in "regime states'', that is our model allows for "regime switching'' among a finite number of regime states. Other aspects of the problem that we address in this thesis are: (1) The portfolio vector of holdings in the risky assets is confined to a given closed and convex constraint set; (2) There is a "state constraint'' in the form of a stipulated almost-sure lower bound on the wealth at close of trade. The combination of constraints represented by (1) and (2) makes the optimization problem quite challenging. The powerful and effective method of {\em auxiliary markets}, of Cvitanic and Karatzas [Ann. Appl. Prob., v.2, 767-818, 1992] for dealing with convex portfolio constraints, does not appear to extend to problems with regime-switching, while the more recent approach of Donnelly and Heunis [SIAM Jour. Control Optimiz., v.50, 2431-2461, 2012], which deals with both regime-switching and the convex portfolio constraints (1), is nevertheless confounded when one adds state constraints of the form (2) to the problem. The reason for this is clear: state constraints of the form (2) typically involve "singular'' Lagrange multipliers which fall well outside the scope of the "well-behaved'' Lagrange multipliers, manifested either as random variables or stochastic processes, which suffice when one is dealing only with portfolio constraints such as (1) above. In these circumstances we resort to an "abstract'' duality approach of Rockafellar and Moreau, which has been applied with considerable success to finite-dimensional problems of stochastic mathematical programming in which singular Lagrange multipliers also naturally arise. The main goal of this thesis is to adapt and extend the Rockafellar-Moreau approach to the stochastic optimal control problem summarized above. We find that this is indeed possible, although some considerable effort is required in view of the infinite dimensionality of the problem. We construct an appropriate space of Lagrange multipliers, synthesize a dual optimization problem, establish optimality relations which give necessary and sufficient conditions for the given optimization problem and its dual to each have a solution with zero duality gap, and use the optimality relations to synthesize an optimal portfolio in terms of the Lagrange multipliers.