# Trimester Seminar

## Thursday, May 16

14:00 - 15:00 Sven Rady (University of Bonn): Breakdowns

Abstract: Joint work with Godfrey Keller (Oxford). We study a continuous-time game of strategic experimentation in which the players try to assess the failure rate of some new equipment or technology. Breakdowns occur at the jump times of a Poisson process whose unknown intensity is either high or low. In marked contrast to existing models, we find that the cooperative value function does not exhibit smooth pasting at the efficient cut-off belief. This finding extends to the boundaries between continuation and stopping regions in Markov perfect equilibria. We characterize the unique symmetric equilibrium, construct a class of asymmetric equilibria, and elucidate the impact of bad versus good Poisson news on equilibrium outcomes.

## Friday, May 17

15:00 - 16:00 Jan Palczewski (University of Leeds): Optimal stopping with a total reward criterion and infinite horizon

Abstract: I will talk about optimal stopping problems for Markov processes with a functional consisting of a running cost and a terminal reward. There is no discounting or the discounting functional is not separated from 1. I will show under what conditions the running cost may play the role of a discounting factor by discouraging from waiting "too long" for an opportunity to stop the process. The solution is very simple when the Markov process is uniformly geometrically ergodic (in essence, when the state space is compact) and it has been known for many years. I will discuss my results towards relaxing the assumption of uniform geometric ergodicity. I will also talk about open problems in that area.

## Thursday, May 23

15:00 - 16:00 Tiziano De Angelis (The University of Manchester): A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis

Abstract: We study a continuous-time, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a one-dimensional, time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investment-disinvestment problem a zero-sum optimal stopping game and characterize its value function through a free-boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment-disinvestment strategy is then shown to be a diffusion reflected at the two boundaries.

16:30 - 17:30 Ekaterina Palamarchuk (CEMI RAS Moscow): Infinite horizon optimization of linear stochastic systems under general time preference

Abstract: We study a stochastic linear economic control system with a quadraticcost function incorporating the agents' time preferences. It is assumed that the time preference can be represented in terms of monotone discount function, which allows to handle the case of negative discounting. Giving a definition of average optimality over an infinite time horizon, we estimate risk from implementing the established optimal control law. The risk estimate serves as an upper bound on random difference between the costs corresponding to the average optimal and an arbitrary admissible control. The pathwise optimality is also discussed. As an example, we investigate a pollution control problem.

## Friday, May 24

15:00 - 16:00 Mark Davis (Imperial College London): Risk management: War on P-measure

## Friday, May 31

15:00 - 16:00 Giorgio Ferrari (Universität Bielefeld): tba

## Thursday, June 6

15:00 - 16:00 Igor V. Evstigneev (University of Manchester): Mathematical Behavioral Finance

Abstract: The purpose of the lecture is to present a new interdisciplinary research area Mathematical Behavioral Finance. Its characteristic feature is the systematic application of behavioral approaches combined with the mathematical modeling of financial markets. The focus of research is on the fundamental questions and problems pertaining to Finance and Financial Economics, especially those related to equilibrium asset pricing and portfolio selection. The models under study reflect the psychology of market participants and go beyond the traditional paradigm of fully rational utility maximization. They do not rely upon restrictive hypotheses (perfect foresight) and avoid using unobservable agents’ characteristics such as individual utilities and beliefs, which makes them amenable to quantitative practical applications. The theory developed may be regarded as a plausible alternative to the classical general equilibrium theory (Walras, Arrow, Debreu, Radner, and others) responding to the challenges of today’s economic and financial reality. The models combine strategic frameworks characteristic for stochastic dynamic games with evolutionary solution concepts, thereby linking two fundamental paradigms of game theory.

Co-authors:

Rabah Amir, Economics Department, University of Iowa

Thorsten Hens, Department of Banking and Finance, University of Zurich

Klaus R. Schenk-Hoppé, School of Mathematics and Business School, University of Leeds, and Norwegian School of Economics, Bergen

Evstigneev-HIM-lecture-June-2013.pdf Igor V. Evstigneev |

## Wednesday, June 26

15:00 - 16:00 Phillip Yam (CUHK, Hong Kong): Linear Quadratic mean-field games

## Thursday, June 27

15:00 - 16:00 & 16:30 - 17:30 Rabah Amir (University of Iowa): Introduction to the theory of supermodular games

## Friday, June 28

11:00 - 12:00 Bruno Ziliotto (University of Toulouse): On the existence of limit value in stochastic games

## Wednesday, July 3

15:00 - 16:00 & 16:30 - 17:30 Sylvain Sorin (Univ Paris 6): Introduction to the theory of evolutionary games (Part I)

Abstract: This lecture will provide a self-contained and general-interest introduction to the theory of evolutionary games and its applications.

## Thursday, July 11

15:00 - 16:00 Ani Guerdjikova (Univ of Cergy-Pontoise): Survival with Ambiguity

Abstract: We analyze a market populated by expected utility maximizers and smooth ambiguity-averse consumers. We study conditions under which ambiguity-averse consumers survive and affect prices in the limit. If ambiguity vanishes with time or if the economy exhibits no aggregate risk, ambiguity-averse consumers survive, but have no long-run impact on prices. In both scenarios, ambiguity-averse consumers are fully insured against ambiguity in equilibrium and, thus, behave as expected utility maximizers with correct beliefs. If ambiguity-averse consumers are not fully insured against ambiguity, they behave as expected utility maximizers with effectively wrong beliefs and an effective discount factor which might be higher or lower than their actual discount factor. Using this insight, we demonstrate that consumers with increasing or constant absolute ambiguity aversion vanish in expectations, whenever the economy faces large persistent ambiguity and aggregate risk. In contrast, consumers with constant relative (and thus, decreasing absolute) ambiguity aversion survive in expectation and with positive probability and have a non-trivial impact on prices in the limit.

## Monday, July 22

15:00 - 16: 00 Thorsten Hens (University of Zurich and Norwegian School of Economics, BergenFinancial Markets): Behavioral Equilibrium and Evolutionary Dynamics

Venue: HIM lecture room on the ground floor

Co-authors: Rabah Amir (University of Iowa), Igor V. Evstigneev (University of Manchester), Klaus R. Schenk-Hoppé (University of Leeds and Norwegian School of Economics, Bergen)

## Thursday, July 25

11:00 - 12:00 Vladimir Viyugin (Institute for Information Transmission Problems): Machine Learning and Unbeatable Strategies

Venue: HIM lecture room on the ground floor

## Friday, August 2

11:00 - 12:00 V. Matthias Gundlach (Technische Hochschule Mittelhessen): Stochastic Chaos

Venue: HIM lecture room on the ground floor

## Monday, August 12

3:00 - 4:00 Rabah Amir (University of Iowa) "Introduction to the theory of supermodular optimization and games"

4:00 - 4:30 Break

4:30 - 5:40 Rabah Amir (University of Iowa) "Introduction to the theory of supermodular optimization and games"

Venue: HIM lecture room on the ground floor

The session is primarily intended for the PhD students (though everyone is welcome) as an introductory lecture to the theory of supermodular optimization and games. The presentation will follow R. Amir's survey article in the Southern Economics Journal (2005). The 4:30-5:30 time slot is subject to demand.

## Tuesday, August 13

3:00 - 4:00Mark Davis (Imperial College London) "Consistent Predictors"

Venue: HIM lecture room on the ground floor

An introductory lecture on prequential statistics and its relevance to risk management. If there is sufficient interest, an additional (informal) brainstorming session on the subject will be held later this week.

## Wednesday, August 14

2:30 - 3:00 (Sophie) Sang Hu (Chinese University of Hong Kong) "Optimal Stopping in Binomial Casino Gambling"

3:10 - 4:00 Tongya Wang (University of Leeds) "Flow of Funds in an Evolutionary Finance Model"

Venue: HIM lecture room on the ground floor

Talks by two PhD students who will present parts of their ongoing work. This session is aimed at those with research interest in the field and all of the junior participants.