Nomura Seminar
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Tue, 11/10/2011 14:15 |
Claudia klupperberg (Munich University of Technology) |
Nomura Seminar  |
Oxford-Man Institute |
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Fri, 21/10/2011 14:15 |
Luciano Campi (Paris 13) |
Nomura Seminar |
DH 1st floor SR |
| Abstract: In this paper we deal with a utility maximization problem at finite horizon on a continuous-time market with conical (and time varying) constraints (particularly suited to model a currency market with proportional transaction costs). In particular, we extend the results in \cite{CO} to the situation where the agent is initially endowed with a random and possibly unbounded quantity of assets. We start by studying some basic properties of the value function (which is now defined on a space of random variables), then we dualize the problem following some convex analysis techniques which have proven very useful in this field of research. We finally prove the existence of a solution to the dual and (under an additional boundedness assumption on the endowment) to the primal problem. The last section of the paper is devoted to an application of our results to utility indifference pricing. This is a joint work with G. Benedetti (CREST). | |||
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Fri, 28/10/2011 14:15 |
Vladmir Vovk (Royal Holloway University of London) |
Nomura Seminar |
DH 1st floor SR |
| The standard approach to continuous-time finance starts from postulating a statistical model for the prices of securities (such as the Black-Scholes model). Since such models are often difficult to justify, it is interesting to explore what can be done without any stochastic assumptions. There are quite a few results of this kind (starting from Cover 1991 and Hobson 1998), but in this talk I will discuss probability-type properties emerging without a statistical model. I will only consider the simplest case of one security, and instead of stochastic assumptions will make some analytic assumptions. If the price path is known to be cadlag without huge jumps, its quadratic variation exists unless a predefined trading strategy earns infinite capital without risking more than one monetary unit. This makes it possible to apply the known results of Ito calculus without probability (Follmer 1981, Norvaisa) in the context of idealized financial markets. If, moreover, the price path is known to be continuous, it becomes Brownian motion when physical time is replaced by quadratic variation; this is a probability-free version of the Dubins-Schwarz theorem. | |||
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Fri, 04/11/2011 14:15 |
Ulrich Horst (Berlin) |
Nomura Seminar |
DH 1st floor SR |
| In this paper we deal with the utility maximization problem with a preference functional of expected utility type. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE). The talk is based on joint work with Ying Hu, Peter Imkeller, Anthony Reveillac and Jianing Zhang. | |||
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Fri, 11/11/2011 14:15 |
William McGhee (Royal Bank Scotland) |
Nomura Seminar |
DH 1st floor SR |
| In the SABR model of Hagan et al. [2002] a perturbative expansion approach yields a tractable approximation to the implied volatility smile. This approximation formula has been adopted across the financial markets as a means of interpolating market volatility surfaces. All too frequently - in stressed markets, in the long-dated FX regime - the limitations of this approximation are pronounced. In this talk a highly efficient conditional integration approach, motivated by the work of Stein and Stein [1991] and Willard [1997], will be presented that when applied to the SABR model not only produces a volatility smile consistent with the underlying SABR process but gives access to the joint distribution of the asset and its volatility. The latter is particularly important in understanding the dynamics of the volatility smile as it evolves through time and the subsequent effect on the pricing of exotic options. William McGhee is Head of Hybrid Quantitative Analytics at The Royal Bank of Scotland and will also discuss within the context of this presentation the interplay of mathematical modelling and the technology infrastructure required to run a complex hybrids trading business and the benefits of highly efficient numerical algorithms." | |||
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Tue, 15/11/2011 14:15 |
Chris Rogers (Cambridge) |
Nomura Seminar |
Oxford-Man Institute |
| The Market Selection Hypothesis is a principle which (informally) proposes that `less knowledgeable' agents are eventually eliminated from the market. This elimination may take the form of starvation (the proportion of output consumed drops to zero), or may take the form of going broke (the proportion of asset held drops to zero), and these are not the same thing. Starvation may result from several causes, diverse beliefs being only one.We firstly identify and exclude these other possible causes, and then prove that starvation is equivalent to inferior belief, under suitable technical conditions. On the other hand, going broke cannot be characterized solely in terms of beliefs, as we show. We next present a remarkable example with two agents with different beliefs, in which one agent starves yet amasses all the capital, and the other goes broke yet consumes all the output – the hungry miser and the happy bankrupt. This example also serves to show that although an agent may starve, he may have long-term impact on the prices. This relates to the notion of price impact introduced by Kogan et al (2009), which we correct in the final section, and then use to characterize situations where asymptotically equivalent pricing holds. | |||
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Fri, 25/11/2011 14:15 |
Mathieu Rosenbaum (University Paris 6) |
Nomura Seminar |
DH 1st floor SR |
| In this work, we consider the hedging error due to discrete trading in models with jumps. We propose a framework enabling to (asymptotically) optimize the discretization times. More precisely, a strategy is said to be optimal if for a given cost function, no strategy has (asymptotically) a lower mean square error for a smaller cost. We focus on strategies based on hitting times and give explicit expressions for the optimal strategies. This is joint work with Peter Tankov. | |||
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Fri, 02/12/2011 14:15 |
John Schoenmakers (Berlin) |
Nomura Seminar |
L3 |
| In this article we propose a novel approach to reduce the computational complexity of the dual method for pricing American options. We consider a sequence of martingales that converges to a given target martingale and decompose the original dual representation into a sum of representations that correspond to different levels of approximation to the target martingale. By next replacing in each representation true conditional expectations with their Monte Carlo estimates, we arrive at what one may call a multilevel dual Monte Carlo algorithm. The analysis of this algorithm reveals that the computational complexity of getting the corresponding target upper bound, due to the target martingale, can be significantly reduced. In particular, it turns out that using our new approach, we may construct a multilevel version of the well-known nested Monte Carlo algorithm of Andersen and Broadie (2004) that is, regarding complexity, virtually equivalent to a non-nested algorithm. The performance of this multilevel algorithm is illustrated by a numerical example. (joint work with Denis Belomestny) | |||
