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

2012/04/01 by Jin Hyuk Choi, Choi, Jin Hyuk, Mihai Ŝırbu +3 · 1 citation
Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1204.0305

openalex publication_date 2012/04/01 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

We revisit the optimal investment and consumption model of Davis and Norman\n(1990) and Shreve and Soner (1994), following a shadow-price approach similar\nto that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of\nthe model without transaction costs, we reformulate and reduce the\nHamilton-Jacobi-Bellman equation for this singular stochastic control problem\nto a non-standard free-boundary problem for a first-order ODE with an integral\nconstraint. Having shown that the free boundary problem has a smooth solution,\nwe use it to construct the solution of the original optimal\ninvestment/consumption problem in a self-contained manner and without any\nrecourse to the dynamic programming principle. Furthermore, we provide an\nexplicit characterization of model parameters for which the value function is\nfinite.\n

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