Mathematical Finance Internal Seminar
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Thu, 20/01/2011 13:00 |
Terry Lyons |
Mathematical Finance Internal Seminar  |
DH 1st floor SR |
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Thu, 27/01/2011 13:00 |
Arend Janssen |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 03/02/2011 13:00 |
Raphael Hauser |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| Optimisation problems involving objective functions defined on function spaces often have a natural interpretation as a variational problem, leading to a solution approach via calculus of variations. An equally natural alternative approach is to approximate the function space by a finite-dimensional subspace and use standard nonlinear optimisation techniques. The second approach is often easier to use, as the occurrence of absolute value terms and inequality constraints poses no technical problem, while the calculus of variations approach becomes very involved. We argue our case by example of two applications in mathematical finance: the computation of optimal execution rates, and pre-computed trade volume curves for high frequency trading. | |||
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Thu, 10/02/2011 13:00 |
Bahman Angoshtari |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| In portfolio management, there are specific strategies for trading between two assets that are cointegrated. These are commonly referred to as pairs-trading or spread-trading strategies. In this paper, we provide a theoretical framework for portfolio choice that justifies the choice of such strategies. For this, we consider a continuous-time error correction model to model the cointegrated price processes and analyze the problem of maximizing the expected utility of terminal wealth, for logarithmic and power utilities. We obtain and justify an extra no-arbitrage condition on the market parameters with which one obtains decomposition results for the optimal pairs-trading portfolio strategies. | |||
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Thu, 17/02/2011 13:00 |
Kevin Burrage |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
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Thu, 24/02/2011 13:00 |
Michael Monoyios |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the expected discounted payoff over all stopping times with regard to an enlarged filtration which includes the inside information. This leads to a stopping problem governed by a time-inhomogeneous diffusion and a call-type reward. Using stochastic flow ideas we establish properties of the value function (monotonicity, convexity in the log-stock price), conditions under which the option value exhibits time decay, and derive the smooth fit condition for the solution to the free boundary problem governing the maximum expected reward. From this we derive the early exercise decomposition of the value function. The resulting integral equation for the unknown exercise boundary is solved numerically and this shows that the insider may exercise the option before maturity, in situations when an agent without the privileged information may not. | |||
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Thu, 03/03/2011 13:00 |
Sam Cohen |
Mathematical Finance Internal Seminar |
L2 |
| Much mathematical work has gone into the creation of time-consistent nonlinear expectations. When we think of implementing these, various problems arise and destroy the beautiful consistency properties we have worked so hard to create. One of these problems is to do with horizon dependence, in particular, where a portfolio's value is considered at a time t+m, where t is the present time and m is a fixed horizon. In this talk we shall discuss various notions of time consistency and the corresponding solution concepts. In particular, we shall focus on notions which pay attention to the space of available policies, allowing for commitment devices and non-markovian restrictions. We shall see that, for any time-consistent nonlinear expectation, there is a notion of time consistency which is satisfied by the moving horizon problem. | |||
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Thu, 10/03/2011 13:00 |
Wei Pan |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
