TY - JOUR
T1 - Hedging in incomplete markets with HARA utility
AU - Duffie, Darrell
AU - Fleming, Wendell
AU - Soner, H. Mete
AU - Zariphopoulou, Thaleia
N1 - Funding Information:
Duffie acknowledges the financial support of the National Science Foundation under NSF SES 90-10062 and the Financial Research Initiative at the Graduate School of Business, Stanford University. H. Mete Soner acknowledges support from the National Science Foundation under NSF DMS-9500940. Wendell Fleming acknowledges financial support from the National Science Foundation under NSF DMS 900038. Thaleia Zariphopoulou acknowledges support from the National Science Foundation under NSF DMS 920486. We are grateful for research assistance from Robert Ashcroft and Flavio Auler and for comments from Ingrid Werner, Ming Huang, and an anonymous referee. We would especially like to thank Steve Shreve for many valuable discussions, and are grateful to Nicole El Karoui, Monique Jeanblanc-Picque, and Hyeng Keun Koo for pointing out errors in an earlier version.
PY - 1997/5
Y1 - 1997/5
N2 - In the context of Merton's original problem of optimal consumption and portfolio choice in continuous time, this paper solves an extension in which the investor is endowed with a stochastic income that cannot be replicated by trading the available securities. The problem is treated by demonstrating, using analytic and, in particular, 'viscosity solutions' techniques, that the value function of the stochastic control problem is a smooth solution of the associated Hamilton-Jacobi-Bellman (HJB) equation. The optimal policy is shown to exist and given in a feedback form from the optimality conditions in the HJB equation. At zero wealth, a fixed fraction of income is consumed. For 'large' wealth, the original Merton policy is approached. We also give a sufficient condition for wealth, under the optimal policy, to remain strictly positive.
AB - In the context of Merton's original problem of optimal consumption and portfolio choice in continuous time, this paper solves an extension in which the investor is endowed with a stochastic income that cannot be replicated by trading the available securities. The problem is treated by demonstrating, using analytic and, in particular, 'viscosity solutions' techniques, that the value function of the stochastic control problem is a smooth solution of the associated Hamilton-Jacobi-Bellman (HJB) equation. The optimal policy is shown to exist and given in a feedback form from the optimality conditions in the HJB equation. At zero wealth, a fixed fraction of income is consumed. For 'large' wealth, the original Merton policy is approached. We also give a sufficient condition for wealth, under the optimal policy, to remain strictly positive.
KW - Hamilton-Jacobi-Bellman equation
KW - Incomplete markets
KW - Optimal portfolio choice
KW - Viscosity solution
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U2 - 10.1016/s0165-1889(97)00002-x
DO - 10.1016/s0165-1889(97)00002-x
M3 - Article
AN - SCOPUS:0031138980
SN - 0165-1889
VL - 21
SP - 753
EP - 782
JO - Journal of Economic Dynamics and Control
JF - Journal of Economic Dynamics and Control
IS - 4-5
ER -