We investigate nodal sets of magnetic Schrödinger operators with zero magnetic field, acting on a non simply connected domain in R 2 . For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a characterisation of the nodal set, and use this to obtain bounds on the multiplicity of the groundstate. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2.

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies -those strategies whose wealth process is a supermartingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utility-based arbitrage, and for the existence of a solution to the primal problem.We consider two utility-based methods which can be used to price contingent claims. Firstly we investigate marginal utility-based price processes (MUBPP's). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims.

Transaction costs, Foreign exchange market, Multivariate utility function, Asymptotic satiability, Optimal portfolio, Duality theory, Lagrange duality, 91B28, 49N15, 49J40, 49J55, G11,

No abstract

In continuous time diffusion models, the optimal strategies to utility maximizations can be obtained by solving a certain partial differential equation. In this paper, we give another proof of this fact in an incomplete market without using the well-known fictitious security arguments. Since we avoid using the fictitious security arguments, we can apply our method to the situations when the markets cannot be completed. We provide an example of such cases where the asset price follows a simple jump process with unpredictable jump sizes and see that we can derive the equation which determines the optimal strategy as usual.