Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Distinguished Research Fellow



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A minimum variance result under Market Conditions This paper introduces the idea of market conditions and analyses an abstract case of these. It is one of a series of papers which explore restrictions on trading within a complete market. This kind of incompleteness is easier to handle than the "dimensional " kind arising when there are more sources of uncertainty than those driving the tradable assets.

Halts in Trading II This another paper on Market Conditions. Here, you are not allowed to trade for certain periods during the life of a contingent claim. We find a trading strategy which allows a hedger to meet their obligations without arbitrage. An interesting point is that the price of this claim does not depend upon when the halts in trading occur, only their aggregate length. Although the results obtained don't reach over to the continuous time case the methods employed do. That material will appear in another paper along with a discussion of random halting times.

Option Pricing withTransaction Costs This takes (another ) look at the question of hedging in the presense of a bid-offer spread. The result has features in common with other work in this area but we have not tried to compare with other work directly. This paper is not yet finished, so don't nick it! I've got almost all the way through the stochastic bid-offer version.

Resources for Students of Mathematical Finance
Problems (and solutions) for Stochastic Processes I