Forthcoming Seminars › Seminar Series

Nomura Seminar

Fri, 22/01/2010
14:15 		Bruno Bouchard (University Paris Dauphine) Nomura Seminar Add to calendar DH 1st floor SR
Optimal Control Under Stochastic Target Constraints
Normal 0 false false false EN-GB X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} We study a class of Markovian optimal stochastic control problems in which the controlled process $ Z^\nu $ is constrained to satisfy an a.s.~constraint $ Z^\nu(T)\in G\subset \R^{d+1} $ $ \Pas $ at some final time $ T>0 $.  When the set is of the form $ G:=\{(x,y)\in \R^d\x \R~:~g(x,y)\ge 0\} $, with $ g $ non-decreasing in $ y $, we provide a Hamilton-Jacobi-Bellman  characterization of the associated value function. It gives rise to a state constraint problem where the constraint can be expressed in terms of an auxiliary value function $ w $ which characterizes the set $ D:=\{(t,Z^\nu(t))\in [0,T]\x\R^{d+1}~:~Z^\nu(T)\in G\;a.s. $ for some $ \nu\} $. Contrary to standard state constraint problems, the domain $ D $ is not given a-priori and we do not need to impose conditions on its boundary. It is naturally incorporated in the auxiliary value function $ w $ which is itself a viscosity solution of a non-linear parabolic PDE.  Applying ideas recently developed in Bouchard, Elie and Touzi (2008), our general result also allows to consider optimal control problems with moment constraints of the form $ \Esp{g(Z^\nu(T))}\ge 0 $ or $ \Pro{g(Z^\nu(T))\ge 0}\ge p $.
Fri, 29/01/2010
14:15 		Marco Frittelli (Milan) Nomura Seminar Add to calendar DH 1st floor SR
Dual Representation of Conditional Quasiconvex Maps
Fri, 05/02/2010
11:00 		Wei Xiong (Princeton University) Nomura Seminar Add to calendar Oxford-Man Institute
Rollover Risk and Credit Risk
This paper models a firm’s rollover risk generated by con.ict of interest between debt and equity holders. When the firm faces losses in rolling over its maturing debt, its equity holders are willing to absorb the losses only if the option value of keeping the firm alive justifies the cost of paying off the maturing debt. Our model shows that both deteriorating market liquidity and shorter debt maturity can exacerbate this externality and cause costly firm bankruptcy at higher fundamental thresholds. Our model provides implications on liquidity- spillover effects, the flight-to-quality phenomenon, and optimal debt maturity structures.
Fri, 12/02/2010
14:15 		Alexander Scheid Nomura Seminar Add to calendar L1
Order book resilience, price manipulation, and Fredholm integral equations
The viability of a market impact model is usually considered to be equivalent to the absence of price manipulation strategies in the sense of Huberman & Stanzl (2004). By analyzing a model with linear instantaneous, transient, and permanent impact components, we discover a new class of irregularities, which we call transaction-triggered price manipulation strategies. Transaction-triggered price manipulation is closely related to the non-existence of measure-valued solutions to a Fredholm integral equation of the first kind. We prove that price impact must decay as a convex decreasing function of time to exclude these market irregularities along with standard price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest. Joint work with Aurélien Alfonsi, Jim Gatheral, and Alla Slynko.
Fri, 19/02/2010
14:15 		Carole Bernard (Waterloo University) Nomura Seminar Add to calendar DH 1st floor SR
Explicit Representation of Cost- Efficient Strategies
Tue, 23/02/2010
14:15 		Frank Riedel (Bielefeld University) Nomura Seminar Add to calendar DH 1st floor SR
Stopping with Multiple Priors and Variational Expectations in Contiuous Time
We develop a theory of optimal stopping problems under ambiguity in continuous time. Using results from (backward) stochastic calculus, we characterize the value function as the smallest (nonlinear) supermartingale dominating the payoff process. For Markovian models, we derive a Hamilton–Jacobi–Bellman equation involving a nonlinear drift term that describes the agent’s ambiguity aversion. We show how to use these general results for search problems and American Options.
Fri, 05/03/2010
14:15 		Geoff Evatt Nomura Seminar Add to calendar L1
Finite Resource Valuations: Myths, Theory and Practise
Abstract: The valuation of a finite resource, be it acopper mine, timber forest or gas field, has received surprisingly littleattention from the academic literature. The fact that a robust, defensible andaccurate valuation methodology has not been derived is due to a mixture ofdifficulty in modelling the numerous stochastic uncertainties involved and thecomplications with capturing real day-to-day mining operations. The goal ofproducing such valuations is not just for accounting reasons, but also so thatoptimal extraction regimes and procedures can be devised in advance for use atthe coal-face. This paper shows how one can begin to bring all these aspectstogether using contingent claims financial analysis, geology, engineering,computer science and applied mathematics.
Fri, 12/03/2010
14:15 		Mete Soner Nomura Seminar Add to calendar DH 1st floor SR
Financial Markets with Uncertain Volatility
 Abstract.  Even in simple models in which thevolatility is only known to stay in two bounds, it is quite hard to price andhedge derivatives which are not Markovian.  The main reason for thisdifficulty emanates from the fact that the probability measures are singular toeach other.  In this talk we will prove a martingale representation theoremfor this market.  This result provides a complete answer to the questionsof hedging and pricing.  The main tools are the theory of nonlinearG-expectations as developed by Peng, the quasi-sure sto chastic artini and thesecond order backward stochastic differential equations.  This is jointwork with Nizar Touzi from Ecole Polytechnique and Jianfeng Zhang fromUniversity of Southern California. 

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