Title: Adaptive Robust Control Under Model Uncertainty
Abstract: We propose a new methodology, called adaptive robust control, for solving a discrete-time Markovian control problem subject to Knightian uncertainty. We apply the general framework to a financial hedging problem where the uncertainty comes from the fact that the true law of the underlying model is only known to belong to a certain family of probability laws. We provide a learning algorithm that reduces the model uncertainty through progressive learning about the unknow system. One of the pillars in the proposed methodology is the recursive construction of the confidence sets for the unknown parameter. This allows, in particular, to establish the corresponding Bellman system of equations.
Mark your calendars for the 5th USA Science & Engineering Festival Expo on April 7-8, 2018! Explore 3,000 hands-on exhibits from the world’s leading scientific and engineering societies, universities, government agencies, high-tech corporations and STEM organizations. The two-day Expo is perfect for children, teens, and families who want to inspire their curious minds.
Where: Walter E. Washington Convention Center
When: Saturday 10 am- 6 pm and Sunday 10 am- 4 pm
Join 350K+ attendees to celebrate science at the Expo and engage in activities with some of the biggest names in STEM. Hear stories of inspiration and courage, participate in mind-boggling experiments and rock out to science during our incredible stage shows.
Date: Monday, April 9th, 2018
Time: 7:00 pm: Enjoy refreshments and snacks with students and faculty.
7:30 pm: The Mathemagics performance begins!
Location: Johns Hopkins University, Homewood Campus; Hodson Hall, Room 110
RSVP: Please fill out the form at: https://tinyurl.com/artbenjhusam
Or E-mail us at firstname.lastname@example.org
Title: Optimal Portfolio under Fractional Stochastic Environment
Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this talk, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index $H \in (0, 1)$). We rigorously establish a first order approximation of the optimal value, when the return and volatility of the underlying asset are functions of a stationary slowly varying fractional Ornstein-Uhlenbeck process. We prove that this approximation can be also generated by the zeroth order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. Furthermore, we extend the discussion to general utility functions, and obtain the asymptotic optimality of this strategy in a specific family of admissible strategies. If time permits, we will also discuss the problem under fast mean-reverting fractional stochastic environment.
Title: On the joint calibration of SPX and VIX options
Abstract: Since VIX options started trading in 2006, many researchers have attempted to build a model for the SPX that jointly calibrates to SPX and VIX options. In 2008, Jim Gatheral showed that a diffusive model could approximately, but not exactly, fit both markets. Later, others have argued that jumps in the SPX were needed to jointly calibrate both markets. We revisit this problem, asking the following questions: Does there exist a continuous model on the SPX that jointly calibrates to SPX options, VIX futures, and VIX options? If so, how to build one such model? If not, why? We present a novel approach based on the SPX smile calibration condition. In the limiting case of instantaneous VIX, the answers are clear and involve the timewise convex ordering of two distributions (local variance and instantaneous variance) and a novel application of martingale transport to finance. The real case of a 30-day VIX is more involved, as time-averaging and projection onto a filtration can undo convex ordering. We observe that in usual market conditions the distribution of VIX^2 in the local volatility model and the market-implied distribution of VIX^2 are not in convex order, and we show that fast mean-reverting volatility models and rough volatility models are able to reproduce this surprising behavior.
Title: Characterizing the Worst-Case Performance of Algorithms for Nonconvex Optimization
Abstract: Motivated by various applications, e.g., in data science, there has been increasing interest in numerical methods for minimizing nonconvex functions. Users of such methods often choose one algorithm versus another due to worst-case complexity guarantees, which in contemporary analyses bound the number of iterations required until a first- or second-order stationarity condition is approximately satisfied. In this talk, we question whether this is indeed the best manner in which to compare algorithms, especially since the worst-case behavior of an algorithm is often only seen when it is employed to minimize pedagogical examples which are quite distinct from functions seen in normal practice. We propose a new strategy for characterizing algorithms that attempts to better represent algorithmic behavior in real-world settings.
Title: Merchant Options of Energy Trading Network
Title: “Statistical network modeling via exchangeable interaction processes”
Many modern network datasets arise from processes of interactions in a population, such as phone calls, e-mail exchanges, co-authorships, and professional collaborations. In such interaction networks, the interactions comprise the fundamental statistical units, making a framework for interaction-labeled networks more appropriate for statistical analysis. In this talk, we present exchangeable interaction network models and explore their basic statistical properties. These models allow for sparsity and power law degree distributions, both of which are widely observed empirical network properties. I will start by presenting the Hollywood model, which is computationally tractable, admits a clear interpretation, exhibits good theoretical properties, and performs reasonably well in estimation and prediction.
In many settings, the series of interactions are structured. E-mail exchanges, for example, have a single sender and potentially multiple receivers. I will introduce hierarchical exchangeable interaction models for the study of structured interaction networks. In particular, I will introduce the Enron model as a canonical example, which partially pools information via a latent, shared population-level distribution. A detailed simulation study and supporting theoretical analysis provide clear model interpretation, and establish global power-law degree distributions. A computationally tractable Gibbs sampling algorithm is derived. Inference will be shown on the Enron e-mail dataset. I will end with a discussion of how to perform posterior predictive checks on interaction data. Using these proposed checks, I will show that the model fits the data well.
Title: Computational Anatomy: Structuring and Searching Shape Spaces.
Abstract: 100 years after the celebrated D’Arcy Thompson’s masterpiece “Growth and Forms”, the modeling and the understanding of both variability and dynamics of related biological shapes are still particularly challenging from both modeling and computational point of view. The luminous idea of his “Theory of Transformations” has been turned within the digital era into a versatile mathematical and computational framework coined as diffeomorphometry and living in the vicinity of riemannian geometry, fluid dynamics, optimal control and statistics. We will discuss about the mathematical side of this framework as well as some of challenges that still need to be faced.