| Speaker | Title | Time | Date | Place |
| Pulak Goswami UT Austin | Recovering an Insider's Information | 2:00pm | Friday 04/25/2013 | RLM 12.166 |
| Abstract: An insider is a market agent who has privileged information about the future state of the market or, more specifically, the future state of an underlying stock. In the filtration enlargement framework, this additional information yields a drift in the perceived dynamics of the stock. Hence the insider's trading strategy can be thought of as result of an optimization problem where the stock has different dynamics. One can ask whether it is possible to recover the drift knowing only the insider's trading strategy. An approach to solving this problem is discussed. | ||||
| Beatrice Acciaio University of Perugia and University of Vienna | Robust Pricing and Hedging: from Mass Transport to Trajectorial Inequalities | 3:30pm | Friday 04/19/2013 | RLM 9.166 |
| Abstract: We will discuss the advantages of relating the robust pricing problem to the theory of mass transportation. Mathematically the crucial difference is that transport plans are required to be martingales in our setting. In particular, we will see how the duality theorem from optimal transport can be used to establish new robust super-replication results. This dual viewpoint also provides new insights on classical martingale inequalities. For instance, we establish a (new) sharp version of the classical Doob maximal inequality. | ||||
| Yu-Jui Huang University of Michigan | Robust Maximization of Asymptotic Growth under Covariance Uncertainty | 3:30pm | Friday 04/12/2013 | RLM 9.166 |
| Abstract: We resolve a question proposed in Kardaras and Robertson (2012): how to invest in a robust growth-optimal way in a market where precise knowledge of the covariance structure of the underlying assets is unavailable. Among an appropriate class of admissible covariance structures, we characterize the optimal trading strategy in terms of a generalized version of the principal eigenvalue of a fully nonlinear elliptic operator and its associated eigenfunction, by slightly restricting the collection of non-dominated probability measures. | ||||
| Daniel Hernandez-Hernandez CIMAT | Some recent result on the value of stochastic differential games | 3:30pm | Friday 03/29/2013 | RLM 9.166 |
| Abstract: In this talk we consider a two player, zero sum stochastic differential game based on a formulation given by Fleming and Souganidis. The saddle point property is introduced, and it is proved that the unique uniformly continuous bounded viscosity solution of the upper Isaacs PDE with boundary condition satisfies such a property. Also, it is shown that approximately optimal Markov strategies can be constructed for both players. | ||||
| Gu Wang Boston Univerity | High-Water Marks and Private Investments for Hedge Fund Managers | 3:30pm | Friday 03/22/2013 | RLM 9.166 |
| Abstract: A hedge fund manager, who receives performance fees proportional to the fund’s profits, invests optimally for both the fund and his own account, as to maximize the expected power utility of personal wealth. If separate and constant investment opportunities are available for each account, it is optimal for the manager to hold a constant fraction of the fund in risky assets, which corresponds to an effective risk aversion between one and the manager’s own risk aversion. For the personal account, the optimal policy is to accumulate performance fees in safe assets, and invest remaining wealth in a constant portfolio corresponding to the manager’s risk aversion. Under the optimal policy, the manager’s welfare is the maximum between the welfare he would obtain from either keeping fees in safe assets only, or investing his personal wealth alone. This result is robust to correlation between investment opportunities, suggesting that the manager does not tend to hedge exposure to the funds’ performance with personal investments. | ||||
| Sergio Pulido Carnegie Mellon | Quadratic BSDEs arising from a price impact model with exponential utility | 3:30pm | Friday 02/22/2013 | RLM 9.166 |
| Abstract: We analyze a price impact model where a large investor wants to trade an illiquid asset with a market maker who quotes prices for this security. In our model, the market maker's preferences are modeled through an exponential utility function and the price impact of the trading strategy of the large investor is derived endogenously through an equilibrium mechanism. We establish a relationship between the equilibrium mechanism and a two-dimensional BSDE with quadratic growth. This allows us to show that an equilibrium exists under certain conditions on the final payoff of the traded asset, the risk aversion coefficient of the market maker and the trading strategy of the large investor. The relationship between the equilibrium mechanism and the two dimensional quadratic BSDE also allows us to study stability and asymptotic behavior with respect to the parameters of the model. This is a joint project with Dmitry Kramkov. | ||||
| Sergey Nadtochiy University of Michigan | OPTIMAL INVESTMENT FOR ALL TIME HORIZONS AND EVOLUTION EQUATIONS WITH A WRONG TIME DIRECTION | 3:30pm | Friday 02/01/2013 | RLM 9.166 |
| Abstract: I will start by reviewing the existing results in the study of forward performance processes, which serve as the optimality criteria for investment problems with multiple time horizons. I, then, show that the existing definition of a forward performance lacks an important component. Having added the missing part of the definition, I develop an axiomatic justification for this theory. In this modified setting, under the additional Markovian assumption on the market, the optimality criterion, as well as the solution to the associated optimization problem, is characterized by the Hamilton-Jacobi-Bellman equation on a semi-finite time interval. The main difficulty in analyzing the latter equation stems from the fact that it ”has time running in a wrong direction”: we need to solve this (backward) parabolic PDE forward in time. Using the existing results on the form of the minimal elements of a Martin boundary of a space-time diffusion, I provide an explicit characterization of all positive solutions to some classes of these (ill-posed) equations. In addition, I show how these results extend the classical Widder’s theorem on the positive solutions of a time-reversed heat equation. | ||||