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Utility Maximization of an Indivisible Market with Transaction Costs

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  • Qingshuo Song
  • G. Yin
  • Chao Zhu

Abstract

This 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.

Suggested Citation

  • Qingshuo Song & G. Yin & Chao Zhu, 2010. "Utility Maximization of an Indivisible Market with Transaction Costs," Papers 1003.2930, arXiv.org.
  • Handle: RePEc:arx:papers:1003.2930
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    References listed on IDEAS

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    1. DeGennaro, Ramon P., 2005. "Market imperfections," Journal of Financial Transformation, Capco Institute, vol. 14, pages 107-117.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    4. Wallace, Neil, 2000. "A model of the liquidity structure based on asset indivisibility," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 55-68, February.
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