A program for Geometric Unity is presented to argue that the seemingly baroque features of the standard model of particle physics are in fact inexorable and geometrically natural when generalizations of the Yang-Mills and Dirac theories are unified with one of general relativity.
Some real resource allocation problems are so large and complex that optimization would computationally infeasible, even with complete information about all the relevant values. For example, the proposal in the US to use television broadcasters' bids to determine which stations go off air to make room for wireless broadband is characterized by hundreds of thousands of integer constraints. We use game theory and auction theory to characterize a class of simple, strategy-proof auctions for such problems and show their equivalence to a class of "clock auctions," which make the optimal bidding strategy obvious to all bidders. We adapt the results of optimal auction theory to reduce expected procurement costs and prove that the procurement cost of each clock auction is the same as that of the full information equilibrium of its related paid-as-bid (sealed-bid) auction.
In this lecture I will exploit a model of asset prices where speculators overconfidence is a source of heterogeneous beliefs and arbitrage is limited. In the model, asset buyers are the most positive investors, but prices exceed their optimistic valuation because the owner of an asset has the option of reselling it in the future to an even more optimistic buyer. The value of this resale option can be identified as a bubble. I will focus on assets with a fixed terminal date, as is often the case with credit instruments. I will show that the size of a bubble satisfies a Partial Differential Equation that is similar to the equation satisfied by an American option and use the PDE to evaluate the impact of parameters such as interest rates or a “Tobin tax” on the size of the bubble and on trading volume.
Lord Desai will discuss how the use of mathematics in economics is as much a result of formalism as of limited knowledge of mathematics. This will relate to his experience as a teacher and researcher and also speak to the current financial meltdown.
``The Utility of Wealth,'', Markowitz's ``other'' 1952 paper, explains observed risk-seeking and risk-avoidance behaviour by a utility function which has deviation from customary wealth, rather than wealth itself, as its argument. It also assumes that utility is bounded above and below.
This talk presents a class (GUW) of functions which generalise
utility-of-wealth (UW) functions. Unlike the latter functions, the
class is too broad to have interesting, verifiable implications. Rather, various subclasses have such implications. A recent paper by Gillen and Markowitz presents notations to specify various subclasses, and explores the properties of some of these.
This talk extends this classification of risk-facing behaviour to non-utility-maximising behaviour as described by Allais and Ellsberg, and formalised by Mark Machina.
The classical expected utility maximisation theory for financial asset allocation is premised on the assumption that human beings when facing risk make rational choices. The theory has been challenged by many observed and repeatable empirical patterns as well as a number of famous paradoxes and puzzles. The prospect theory in behavioural finance use cognitive psychological techniques to incorporate anomalies in human judgement into economic decision making. This lecture explains the interplay between risk and human judgement, and its impact on dynamic asset allocation via mathematically establishing and analysing a behavioural portfolio choice model.