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Abstracts

• Leif Andersen
  Title: Real Time American Option Pricing (Slides)
  Abstract: Recently, we introduced a new numerical technique for the pricing of American options with smooth dividends, besting the speed of traditional approaches by about 4 orders of magnitude. Here, we discuss the extension to American options with discrete dividends, paying special attention to the (non-classical) case where the funding spread of the stock is non-zero. We list some new theoretical and numerical results, and discuss the circumstances in which the performance gains from the smooth-dividend algorithms carry over to a setting with discrete dividends.
   
• Alain Bélanger
  Title: Over-the-Counter Market Models (Slides)
  Abstract: We develop an approach, inspired by the work of M. Kac in the statistical physics of gases, where the random matching of a large population of investors is asymptotically independent. We start with a sequence of dynamical systems of N interacting components and as N grows large we show that the probability gets very small that a component has interacted more than once, directly or indirectly, with any other component. This fundamental property enables us to link the microscopic and macroscopic levels using results from the theory of continuous-time Markov chains. We then obtain the solution of the non-linear evolution equation, in the case of a single interacting kernel, by a series construction we call extended Wild sums. We show afterwards how to retain the explicit nature of the solution when there are more than one type of interactions.
  Joint work with G. Giroux and N. Ndouné
   
• Dimitri P. Bertsekas
  Title: Semicontractive Models in Abstract Dynamic Programming
  Abstract: Abstract dynamic programming (DP for short) aims at a unified and economical development of the core theory and algorithms of total cost sequential decision problems, based on the strong connections of the subject with fixed point theory. The analysis focuses on the abstract mapping that underlies DP and defines the mathematical character of the associated problem. As shown by research in the 60s and the 70s, the nature of the analytical and algorithmic DP theory is determined primarily by the presence or absence of monotonicity and contraction properties, and (except for measurability issues) the rest of the problem's structure is largely inconsequential.
  We will review this theory, and its manifestations in discounted, positive and negative cost DP. We will then discuss a new model, semicontractive DP, exemplified by the popular stochastic shortest path problems, where some but not all policies are contractive. A key notion for analysis of this model is regularity of a policy, which we use to investigate the existence and uniqueness of solution of the abstract form of Bellman's equation, and the convergence properties of value and policy iteration. We apply our approach to a variety of models, including deterministic, stochastic, and minimax shortest path problems, positive and negative cost DP, stochastic optimal control with mixed positive and negative costs per stage, and multiplicative cost problems.
   
• René Carmona
  Title: Recent Developments in the Probabilistic Theory of Mean Field Games (Slides)
   
• Peter Carr
  Title: Applying Convex Duality To Option Pricing (Slides)
  Abstract: The absence of arbitrage forces option prices to be convex in strike price. In Markovian models, option prices are typically also convex in their underlying asset price. We use convex duality to explore the implications of these well-known results.
   
• Pierre Collin-Dufresne
  Title: Insider Trading, Stochastic Liquidity and Equilibrium Prices (Slides)
  Abstract: We extend Kyle's (1985) model of insider trading to the case where noise trading volatility follows a general stochastic process. In equilibrium, price impact and price volatility are stochastic, even though the fundamental value is constant. 'Excess stochastic volatility' may arise because non-payoff relevant shocks can affect price volatility as insiders choose to trade more aggressively (and thus more information is revealed) when noise traders are more active and price impact is lower. This also generates a positive relation between price volatility and trading volume.
  Joint work with Vyacheslav Fos
   
• Jakša Cvitanić
  Title: Achieving Efficiency in Dynamic Contribution Games (Slides)
  Abstract: We analyze a game in which a group of agents exert costly effort over time to make progress on a project, which is completed once the cumulative efforts reach a pre-specified threshold, at which point it generates a lump sum payoff. We characterize a budget balanced mechanism which at every moment induces each agent to exert the first best effort level as the outcome of a Markov Perfect Equilibrium, thus eliminating the free-rider problem. This mechanism specifies for each agent flow payments that he must make while the project is in progress, and a reward that is payable upon completion.
  Joint work with George Georgiadis
   
• Freddy Delbaen
  Title: Risk Measures, Orlicz spaces and Mackey topology (Slides)
  Abstract: For a risk measure defined on L^∞, there is a stronger continuity property which can be translated as (sequential) continuity on the bounded sets for the Mackey topology induced by L¹. This is a more complicated way of saying that the risk measure satisfies a dominated convergence theorem. It was proved (by Cheridito and Li) that this implies a continuity property on the whole space (not just on bounded sets). One can ask whether such a phenomenon exists for convex functions defined on the dual of an arbitrary Banach space. There are several extensions possible. The general result, although straightforward in convex function theory, seems new. Whether sequential continuity implies continuity is related to a property called strongly weakly compactly generated (SWCG). There are counterexamples for spaces not satisfying the SWCG property. In the talk I will put emphasis on the relation between risk measures, Orlicz spaces and Mackey topology.
   
• Darrell Duffie
  Title: Benchmarks in Search Markets (Slides)
  Abstract: We analyze the role of benchmarks in over-the-counter markets subject to search frictions. The publication of a benchmark can, under conditions, raise total social surplus by (i) increasing the volume of beneficial trade, (ii) facilitating more efficient trade matching between dealers and customers, and (iii) reducing total search costs. Although the improvement in market transparency caused by benchmarks may lower dealer profit margins on each trade, dealers may nevertheless introduce a benchmark such as LIBOR in order to encourage greater market participation by investors. In some cases, low-cost dealers may introduce a benchmark in order to increase their market share through reducing entry by high-cost dealers, a further source of efficiency gain.
  Joint work with Piotr Dworczak and Haoxiang Zhu
   
• Bruno Dupire
  Title: Tradable Estimates of Quadratic Variation (Slides)
  Abstract: There are many estimates of historical volatility, based on time samples, price level samples, on high and low. I define an estimate as "tradable" if it is attainable from a static position in options a dynamic trading of the underlying. I characterize the unbiased tradable estimates, show that the difference of two of them is a costless dynamic strategy and show how the daily/weekly trade performs on various time periods.
  The usual estimates based on high and low are not tradable. Surprisingly, it is not because high and low are not stopping times but because they not not depend quadratically on the final value. I introduce a new high and low based estimate that is tradable and unbiased.
   
• Julien Hugonnier
  Title: Heterogeneity in decentralized markets
  Abstract: We study a search and bargaining model of an asset market, where investors' heterogeneous valuations for the asset are drawn from an arbitrary distribution. Our solution technique renders the analysis fully tractable and allows us to provide a full characterization of the equilibrium, in closed-form, both in and out of steady-state. We use this characterization for two purposes. First, we establish that the model can naturally account for a number of stylized facts that have been documented in empirical studies of over-the-counter asset markets. In particular, we show that heterogeneity among market participants implies that assets are reallocated through intermediation chains, ultimately producing a core-periphery trading network and non-trivial distributions of prices and trading times. Second, we show that the model generates a number of novel results that underscore the importance of heterogeneity in decentralized markets. We highlight two: first, heterogeneity magnifies the price impact of search frictions; and second, search frictions have larger effects on price levels than on price dispersion. Hence, quantifying the price discount or premium created by search frictions based on observed price dispersion can be misleading.
  Joint work with Pierre Olivier Weill and Ben Lester
   
• Karel Janeček
  Title: Democracy 2.1 (Slides)
  Abstract: Modern democracies have traditionally relied on the principle of "one man one vote" to guarantee fair and equal access to the political process. We argue that, in the 21st century, the crucial question is not who votes, but how we vote. It is possible to create a voting system with uniform voting rights in which consensus can triumph over polarization and voters are more motivated and engaged. Democracy 2.1 has precisely this effect. D21 is a universally applicable system to revolutionize group decision-making processes. In the past year, we have successfully piloted D21 in partnership with cities, corporations and NGOs in Europe as well as the US. D21 points the way toward a worldwide renewal and qualitative upgrade of the democratic process.
   
• Ioannis Karatzas
  Title: Explosions And Arbitrage (Abstract / Slides)
   
• John Lehoczky
  Title: Asymptotic Analysis of Real-Time Queues (Slides)
  Abstract: This talk will review joint work with Steve Shreve and many collaborators concerning the asymptotic analysis of real-time queues, namely queues in which the tasks have deadlines. The performance measure of such a system focuses on the ability of the system to meet task deadlines rather than more traditional measures such as waiting time, queue length or server utilization. Consequently, traditional disciplines such as FIFO are not appropriate. Real-time queue disciplines like earliest deadline first must keep track of customer lead-times, which change dynamically, so the state of the system, called the lead-time profile, is high dimensional. A heavy traffic analysis is presented for the earliest deadline first queue discipline. The analysis decomposes the behavior of the queue into two parts: the number in the system (which converges weakly to a reflected Brownian motion with drift) and the lead-time profile given the queue length. This lead-time profile has a limit that is a nonrandom function of the limit of the scaled queue length process. Simulations show that the resulting approximations are remarkably accurate. A number of extensions to the work will be discussed including task reneging and queueing networks.
   
• Jin Ma
  Title: Conditional Mean-field SDEs and Some Related Stochastic Control Problems
  Abstract: We study a class of conditional mean-field SDEs (CMFSDEs, for short), in which the reference dynamics also involves the conditional law of the solution, hence "closed-loop" in nature. We investigate the well-posedness of the CMFSDEs in two particular settings, along with a non-Markovian stochastic control problems with partial observations and a problem regarding the "strategic insider trading equilibrium models". In the former we consider a McKean-Vlasov stochastic control problem, with added aspects of path-dependence and partial observation. We prove Pontryagin's Stochastic Maximum Principle and study the associated mean-field type Backward SDEs. In the latter we provide a rigorous theoretical basis for a general dynamic Kyle-Back type strategic insider trading equilibrium model in which the insider is allowed to have dynamic information of an asset rather than only the "long-lived" static ones; and tie the loose ends of some heuristic arguments in the literature of this problem.
  Joint work with Rainer Buckdahn, Juan Li, Yonghui Zhou, and Rentao Sun
   
• Walter Schachermayer
  Title: Duality Methods in Portfolio Optimization (Slides)
  Abstract: We review the development of this line of research where Steve Shreve made major contributions and present some recent results.
   
• Martin Schweizer
  Title: Valuation under minimal economic conditions
  Abstract: We propose a systematic approach to the valuation of contingent claims in a general semimartingale model with minimal assumptions and with clear economic motivation. Our starting point is the observation that even in the classic Black-Scholes framework, many (textbook) derivations of option pricing formulas use "absence-of-arbitrage" arguments without being explicit about the precise assumptions they impose. In order to understand this better and from a different perspective, we develop a systematic approach that also works in models with bubbles.
  Joint work with Martin Herdegen (ETH Zurich)
   
• Mihai Sîrbu
  Title: Asymptotic Perron's method in stochastic games and control (Slides)
  Abstract: We introduce a modification of Perron's method, where semi-solutions are considered in a carefully defined asymptotic sense. With this definition, we can show, in a rather elementary way, that in a zero-sum game or a control problem (with or without model uncertainty), the value function over all strategies coincides with the value function over Markov strategies discretized in time. With a minor modification, the method produces a value and approximate discretized Markov saddle points for an asymmetric game of feedback strategies vs. counter-strategies.
   
• Josef Teichmann
  Title: A new perspective on the proof of the fundamental theorem of asset pricing (Slides)
  Abstract: By means of supermartingale deflators we are able to shed some new light on the proof of the fundamental theorem of asset pricing for small and large financial markets.
  Joint work with Christa Cuchiero and Irene Klein
   
• Nizar Touzi
  Title: Exact simulation of stochastic differential equations (Slides)
   
• Kim Weston
  Title: When is the Dual Optimizer a Martingale?
  Abstract: An unpleasant qualitative feature of the general theory of optimal investment is that the dual optimizer may not correspond to the density of a martingale measure. The existence of such a dual optimal martingale measure is often desirable. For instance, in pricing theory, its existence is equivalent to the uniqueness of marginal utility based prices for all bounded contingent claims. In this work, we show that the dual optimizer is the density of a martingale measure if one can find a p>1 such that
  (i) There is a martingale measure whose density process satisfies the Muckenhoupt (Ap) condition from BMO spaces;
  (ii) The relative risk-aversion of the utility function is bounded below by 1/q=1-1/p and above by a constant.
  In particular, condition (i) holds for the minimal martingale measure if the market price of risk is bounded. Finally, we present a counterexample showing that in some sense this (Ap) condition is necessary.
  Joint work with Dmitry Kramkov.
   
• Gan-Lin Xu
  Title: Continuous Time Finance and Mean-Variance in Post-Retirement Planning (Slides)
  Abstract: Financial planning in post-retirement should be an relatively easier subject compared to derivative modeling using continuous time finance. That is not the case. Mathematicians are very satisfied with solving HBJ equations arising from maximizing expected utility of consumption/portfolio selection problem. Practitioners mainly focus on maximizing the fixed spending rate. This talk will use mean-variance analysis to bridge the gap between the two groups.
   
• Gordan Žitković
  Title: Incomplete stochastic equilibria with exponential utilities under "smallness" (Slides)
  Abstract: We study existence and uniqueness of continuous-time stochastic Radner equilibria with incomplete markets. These are shown to exist and are unique under several classical - and one new - assumptions of "smallness" type. A central role in our analysis is played by a fully-coupled nonlinear system of quadratic BSDEs.
  Joint work with C. Kardaras and H. Xing
   

Posters

• Akal, Orhan (Florida State University)
  Agent Based Modeling for Stock Market with heterogeneous traders trading over multiple stocks
   
• Almualim, Anwar (University of Leicester, UK)
  Cooperative Investment in multi-period on GARCH with dynamic programming Approach
   
• Arora, Neha (Department of Commerce, Delhi School of Economics, University of Delhi)
  Classifying Indian Bull and Bear Markets using Bry & Boschan Algorithm
   
• Bai, Xi (Lehigh University)
  Least-squares approach to risk parity in portfolio selection
   
• Bernardinelli, Luca (Dublin City University)
  A Dynamic Asymmetric Information Equilibrium
   
• Bimbabou Maboulou, Alma Prell (North West University)
  Credit Derivative Valuation and Parameter Estimation for CIR and Vasicek-type models with Reference to South Africa Bonds
   
• Bruggeman, Cameron (Columbia University)
  Dynamics of Large Competing Brownian Particle Systems
   
• Cerenzia, Mark (Princeton University)
  Symplectic Plancherel Growth, Anisotropic KPZ Universality, and Interlaced Reflecting Brownian Motions
   
• Chen, Peng-Chu (Purdue University)
  Liability Concentration and Systemic Losses in Financial Networks
   
• Chen, Tao (Illinois Institute of Technology)
  Market making via sub-scale invariant Dynamic Acceptability Indices
   
• Cheng, Wan-Schwin (Columbia University)
  Systemic Risk: The Dynamics Under Central Clearing
   
• Cohen, Albert (Michigan State University)
  Pricing Recovery Risk in Bonds and other Credit Products
   
• Cui, XueCan (University of Luxembourg)
  Option pricing models with underlying time-varying Lévy processes
   
• Deshpande, Amogh (U. Liverpool)
  On the role of Föllmer-Schweizer minimal martingale measure in Risk Sensitive control Asset Management
   
• Donnelly, Ryan (EPFL)
  Algorithmic Trading Under the Effects of Volume Order Imbalance
   
• Englezos, Nikolaos (University of Piraeus)
  Expectations Modelling in Economics and (Controlled) Infinite-Horizon FBSDEs
   
• Fahim, Arash (Florida State University)
  Robust hedging under portfolio constraint and price impact
   
• Garreau, Pierre (Goethe University)
  A spectral element framework for option pricing under general exponential Lévy processes
   
• Goswami, Pulak (University of Texas at Austin)
  Recovering the Payoff Structure of a Utility Maximizing Agent
   
• Gu, Lingqi (Faculty of Mathematics, University of Vienna)
  On the dual problem of utility maximization in incomplete markets
   
• Herdegen, Martin (ETH Zürich)
  Sensitivity of Optimal Consumption Streams
   
• Herrmann, Sebastian (ETH Zürich)
  Hedging with small volatility uncertainty
   
• Hussain, Azmat (North Carolina State University)
  An Infinite Time Horizon Portfolio Optimization Model with Delays
   
• Ikpe, Dennis (University of Cape Town and University of Michigan)
  Information Based Model Of Default Risk
   
• Keller, Christian (University of Southern California)
  Pathwise Viscosity Solutions of Stochastic PDEs
   
• Lin, Yiqing (Faculty of Mathematics, University of Vienna)
  On The Dual Problem Of Utility Maximization In Incomplete Markets
   
• Lux, Thibaut (Technical University Berlin, Germany)
  Dependence Uncertainty, Frechet Bounds and Model-Free Option Pricing
   
• Mastrolia, Thibaut (Université Paris Dauphine)
  Malliavin differentiability of BSDEs and density analysis
   
• Meireles Rodrigues, Andrea Sofia (School of Mathematical Sciences, Dublin City University)
  Continuous-Time Portfolio Optimisation for a Behavioural Investor
   
• Miller, Christopher (University of California, Berkeley)
  Stochastic control approach to model-free price bounds for VIX derivatives
   
• Mostovyi, Oleksii (UT Austin)
  An Expansion in the Model Space in the Context of Utility Maximization
   
• Munk, Alexander (University of Michigan)
  An α-Stable Limit Theorem Under Sublinear Expectation
   
• Nam, Kihun (Rutgers University)
  Solving backward stochastic equation using Banach and Schauder-type Fixed Point Theorems
   
• Nguyen, Duy D. (Massachusetts College of Liberal Arts)
  A Finite Horizon Optimal Consumption and Portfolio Selection Problem In A Regime Switching Jump Diffusion Model
   
• Petersen, Ethan (Rose-Hulman Institute of Technology)
  The Stock Price Effect of Apple Keynotes
   
• Rayskin, Victoria (MIT)
  Regions of equilibria of two-sided market
   
• Ren, Dan (University of Dayton)
  Optimal Consumption and Investment with Shortfall Aversion and Resilience
   
• Saplaouras, Alexandros (Technical University of Berlin)
  Towards a robustness result for BSDEs with jumps
   
• Szabo, David Zoltan (The University of Manchester)
  American put options for power system balancing
   
• Thamrongrat, Nopporn (Institute of Applied Mathematics, University of Heidelberg, Germany)
  Positive semi-definite estimators using subsampling in high frequency data
   
• Tunyavetchakit, Sophon (Institute of Applied Mathematics, Heidelberg University, Germany)
  Nonparametric estimation for spot volatility of model with Poisson sampling under market microstructure noise
   
• Verdiyan, Vardan (Cornell University)
  Portfolio Construction under Share Restrictions
   
• Wang, Gu (University of Michigan at Ann Arbor)
  Quantile Hedging in a Semi-Static Market with Model Uncertainty
   
• Weston, Kim (Carnegie Mellon)
  Stability of Utility Maximization in Nonequivalent Markets
   
• Wildman, Mackenzie (Lehigh University)
  A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivatives
   
• Yan, Minghan (Columbia University)
  Stochastic Integral Equation for Walsh Semimartingales
   
• Yang, Junjian (Faculty of Mathematics, University of Vienna)
  On the dual problem of utility maximization in incomplete markets
   
• Yu, Xiang (The University of Michigan)
  On the market viability under proportional transaction costs
   
• Zeng, Pingping (University of Vienna)
  Transform methods for pricing exotic options and variance derivatives under the 3/2 model
   
• Zhang, Yuchong (University of Michigan)
  Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty
   
• Zhong, Jie (University of Central Florida)
  Parametrix method for skew diffusions
   

• Carnegie Mellon University
• Department of Mathematical Sciences
• MSCF Program