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    A shadow-price approach of the problem of optimal investment/consumption with proportional transaction costs and utilities of power type

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    CHOI-DISSERTATION.pdf (1.378Mb)
    Date
    2012-08
    Author
    Choi, Jin Hyuk, 1983-
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    Abstract
    We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. By analyzing the properties of the free boundary problem, we provide an explicit characterization of model parameters for which the value function is finite. Furthermore, we prove that the value function, as well as the slopes of the lines demarcating the no-trading region, can be expanded as a series of integer powers of [lambda superscript 1/3]. The coefficients of arbitrary order in this expansion can be computed.
    Department
    Mathematics
    Description
    text
    Subject
    Optimal consumption
    Singular stochastic control
    Transaction costs
    Shadow prices
    URI
    http://hdl.handle.net/2152/ETD-UT-2012-08-5926
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    • facebook
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    © The University of Texas at Austin