Past Nomura Lecture

The most valuable asset that people in a sovereign state can have is good, sustainable governance. Setting up a system of good, sustainable governance is not easy. The big and well-known problem is time inconsistency of optimal policies. A mechanism that has proven valuable in mitigating the time inconsistency problem is rule by law. The too-big-to-fail problem in banking is the result of the time inconsistency problem. In this lecture I will argue there is an alternative financial system that is not subject to the too-big-to-fail problem. The alternative arrangement I propose is a pure transaction banking system. Transaction banks are required to hold 100$\%$ interest bearing reserves and can pay tax-free interest on demand deposits. With this system, there cannot be a bank run as there is no place to run to. Mutual arrangements would finance all business investment, which is not currently the case.

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.

In the Examination Schools.

Over the last decades, advanced probabilistic methods have played an increasing role in Finance, both in Academia and in the financial industry. In view of the recent financial crisis it has been asked to which extent "misplaced reliance on sophisticated maths" has been part of the problem. We will focus on the foundational issue of model uncertainty, also called "Knightian uncertainty". This will be illustrated

by the problem of quantifying financial risk. We discuss recent advances

in the theory of convex risk measures and a corresponding robustification of classical problems of optimal portfolio choice, where model uncertainty is taken into account explicitly.

Biography: Hans Follmer is Professor Emeritus of Mathematics at Humboldt-Universitat zu Berlin, Andrew D. White Professor-at-Large at Cornell University, and Visiting Professor at the National University of Singapore. Before joining Humboldt University in 1994, he has been professor at the universities of Frankfurt and Bonn and at ETH Zurich.

Hans Follmer is widely known for his contributions to probability theory and mathematical finance. He received numerous awards, including the Prix Gay-Lussac/Humboldt of the French Government, the Georg-Cantor medal of the German Mathematical Society, and a honorary degree of the University Paris-Dauphine. He is a member of the Berlin-Brandenburgische Akademie der Wissenschaften, the German National Academy of Sciences Leopoldina, and the European Academy of Sciences Academia Europaea.

In the Said Business School

The covariance between nominal bonds and stocks has varied considerably over recent decades and has even switched sign. It has been predominantly positive in periods such as the late 1970s and early 1980s when the economy has experienced supply shocks and the central bank has lacked credibility. It has been predominantly negative in periods such as the 2000s when investors have feared weak aggregate demand and deflation. This lecture discusses the implications of changing bond risk for the shape of the yield curve, the risk premia on bonds, and the relative pricing of nominal and inflation-indexed bonds.

In the Said Business School

As the shockwaves of the financial crisis of 2008 propagate throughout the global economy, the "blame game" has begun in earnest, with some fingers pointing to the complexity of certain financial securities, and the mathematical models used to manage them. In this talk, I will review the evidence for and against this view, and argue that a broader perspective will show a much different picture.Blaming quantitative analysis for the financial crisis is akin to blaming F = MA for a fallen mountain climber's death. A more productive line of inquiry is to look deeper into the underlying causes of financial crisis, which ultimately leads to the conclusion that bubbles, crashes, and market dislocation are unavoidable consequences of hardwired human behavior coupled with free enterprise and modern capitalism. However, even though crises cannot be legislated away, there are many ways to reduce their disruptive effects, and I will conclude with a set of proposals for regulatory reform.

``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.