Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs

Details Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs

2012-04-02

arxiv.org/abs/1204.0305v1

Economy

Quantitative Finance

Portfolio Management

31 pages, 20 figures

Scientific paper

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. Furthermore, we provide an explicit characterization of model parameters for which the value function is finite.

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