Mathematical Finance Internal Seminar
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Thu, 16/10/2008 13:00 |
John Quah (Economics) |
Mathematical Finance Internal Seminar  |
DH 1st floor SR |
| We identify a natural way of ordering functions, which we call the interval dominance order, and show that this concept is useful in the theory of monotone comparative statics and also in statistical decision theory. This ordering on functions is weaker than the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so our monotone comparative statics results apply in some settings where the single crossing property does not hold. For example, they are useful when examining the comparative statics of optimal stopping time problems. We also show that certain basic results in statistical decision theory which are important in economics - specifically, the complete class theorem of Karlin and Rubin (1956) and the results connected with Lehmann's (1988) concept of informativeness – generalize to payoff functions that obey the interval dominance order. | |||
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Thu, 30/10/2008 13:00 |
Xunyu Zhou (Oxford) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| A new portfolio choice model in continuous time is formulated and solved, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as the decision variable. This formulation covers and leads to solutions to many existing and new models including expected utility maximisation, mean-variance, goal reaching, VaR and CVaR, Yaari's dual model, Lopes' SP/A model, and behavioural model under prospect theory. | |||
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Thu, 13/11/2008 13:00 |
Sam Howison |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| I shall discuss a number of problems to do with approximating the value function of an American Put option in the Black-Scholes model. This is essentially a variant of the oxygen-consumption problem, a parabolic free boundary (obstacle) problem which is closely related to the Stefan problem. Having reviewed the short-time behaviour from the perspective of ray theory, I shall focus on constructing approximations in the case when there is a discretely paid dividend yield. | |||
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Thu, 27/11/2008 13:00 |
Jan Obloj |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| I consider the problem of maximising the final utility of a portfolio which is constrained to satisfy the draw-down condition, i.e. the current value of the portfolio can not drop below a pre-specified funciton of its running maximum. It turns out that martingale techniques yield an explicit and rather elegant solution. The so- called Azema-Yor processes appear naturally and I take some time to introduce this class and discuss some of their remarkable properties. In particular, I show how they can be characterised as (unique, strong) solutions to SDEs called the Bachelier Eq and the Draw-Down Eq. The talk is based (in particular) on a joint work with L. Carraro, N. El Karoui and A. Meziou. | |||
