Utility Maximization of an Indivisible Market with Transaction Costs
AbstractThis work takes up the challenges of utility maximization problem when the market is indivisible and the transaction costs are included. First there is a so-called solvency region given by the minimum margin requirement in the problem formulation. Then the associated utility maximization is formulated as an optimal switching problem. The diffusion turns out to be degenerate and the boundary of domain is an unbounded set. One no longer has the continuity of the value function without posing further conditions due to the degeneracy and the dependence of the random terminal time on the initial data. This paper provides sufficient conditions under which the continuity of the value function is obtained. The essence of our approach is to find a sequence of continuous functions locally uniformly converging to the desired value function. Thanks to continuity, the value function can be characterized by using the notion of viscosity solution of certain quasi-variational inequality.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1003.2930.
Date of creation: Mar 2010
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-03-28 (All new papers)
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