Nomura Seminar
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Tue, 12/10/2010 14:15 |
Tomas Bjork (Columbia University/Stockholm School of Economics) |
Nomura Seminar  Oxford-Man Institute Working Seminar |
Eagle House |
| "We present a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for subgame perfect Nash equilibrium points. For a general controlled Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman equation, in the form of a system of non-linear equations. We give some concrete examples, and in particular we study the case of mean variance optimal portfolios with wealth dependent risk aversion" | |||
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Tue, 12/10/2010 14:15 |
Ioannis Karatzas |
Nomura Seminar |
Eagle House |
| We introduce and study ergodic multidimensional diffusion processes interacting through their ranks; these interactions lead to invariant measures which are in broad agreement with stability properties of large equity markets over long time-periods. The models we develop assign growth rates and variances that depend on both the name (identity) and the rank (according to capitalization) of each individual asset. Such models are able realistically to capture critical features of the observed stability of capital distribution over the past century, all the while being simple enough to allow for rather detailed analytical study. The methodologies used in this study touch upon the question of triple points for systems of interacting diffusions; in particular, some choices of parameters may permit triple (or higher-order) collisions to occur. We show, however, that such multiple collisions have no effect on any of the stability properties of the resulting system. This is accomplished through a detailed analysis of intersection local times. The theory we develop has connections with the analysis of Queueing Networks in heavy traffic, as well as with models of competing particle systems in Statistical Mechanics, such as the Sherrington-Kirkpatrick model for spin-glasses. | |||
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Fri, 22/10/2010 14:15 |
Ronnie Sircar (Princeton University) |
Nomura Seminar |
DH 1st floor SR |
| The theory and computation of convex measures of financial risk has been a very active area of Financial Mathematics, with a rich history in a short number of years. The axioms specify sensible properties that measures of risk should possess (and which the industry's favourite, value-at-risk, does not). The most common example is related to the expectation of an exponential utility function. A basic application is hedging, that is taking off-setting positions, to optimally reduce the risk measure of a portfolio. In standard continuous-time models with dynamic hedging, this leads to nonlinear PDE problems of HJB type. We discuss so-called static-dynamic hedging of exotic options under convex risk measures, and specifically the existence and uniqueness of an optimal position. We illustrate the computational challenge when we move away from the risk measure associated with exponential utility. Joint work with Aytac Ilhan (Goldman Sachs) and Mattias Jonsson (University of Michigan). | |||
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Fri, 29/10/2010 14:15 |
Matheus Grasselli (McMaster University Canada) |
Nomura Seminar |
DH 1st floor SR |
| A stock loan is a contract between two parties: the lender, usually a bank or other financial institution providing a loan, and the borrower, represented by a client who owns one share of a stock used as collateral for the loan. Several reasons might motivate the client to get into such a deal. For example he might not want to sell his stock or even face selling restrictions, while at the same time being in need of available funds to attend to another financial operation. In Xia and Zhou (2007), a stock loan is modeled as a perpetual American option with a time varying strike and analyzed in detail within the Black-Scholes framework. In this paper, we extend the valuation of such loans to an incomplete market setting, which takes into account the natural trading restrictions faced by the client. When the maturity of the loan is infinite we obtain an exact formula for the value of the loan fee to be charged by the bank based on a result in Henderson (2007). For loans of finite maturity, we characterize its value using a variational inequality first presented in Oberman and Zariphopoulou (2003). In both cases we show analytically how the fee varies with the model parameters and illustrate the results numerically. This is joint work with Cesar G. Velez (Universidad Nacional de Colombia). | |||
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Fri, 05/11/2010 14:15 |
Hansjoerg Albrecher (Universite de Lausanne) |
Nomura Seminar |
DH 1st floor SR |
| In this talk a number of identities will be discussed that relate to the event of level crossing of certain types of stochastic processes. Some of these identities are surprisingly simple and have interpretations in surplus modelling of insurance portfolios, the design of taxation schemes, optimal dividend strategies and the pricing of barrier options. | |||
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Fri, 12/11/2010 14:15 |
Yuri Kabanov (Universite de Franche-Compte) |
Nomura Seminar |
DH 1st floor SR |
| The talk will be devoted to criteria of absence of arbitrage opportunities under small transaction costs for a family of multi-asset models of financial market. | |||
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Fri, 19/11/2010 14:15 |
Guy Barles (Universite Francois Rablelais) |
Nomura Seminar |
DH 1st floor SR |
| Abstract: describe several results on the convergence of approximation schemes for possibly degenerate, linear or nonlinear parabolic equations which apply in particular to equations arising in option pricing or portfolio management. We address both the questions of the convergence and the rate of convergence. | |||
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Fri, 26/11/2010 14:15 |
CANCELLED |
Nomura Seminar |
DH 1st floor SR |
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Fri, 03/12/2010 14:15 |
Kees Oosterlee (Delft University of Technology) |
Nomura Seminar |
L3 |
| In this presentation we discuss the Heston model with stochastic interest rates driven by Hull-White or Cox-Ingersoll-Ross processes. We present approximations in the Heston-Hull-White hybrid model, so that a characteristic function can be derived and derivative pricing can be efficiently done using the Fourier Cosine expansion technique. This pricing method, called the COS method, is explained in some detail. We furthermore discuss the effect of the approximations in the hybrid model on the instantaneous correlations, and check the influence of the correlation between stock and interest rate on the implied volatilities. | |||
