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Optimal Investment With Undiversifiable Income Risk
Author(s) -
Duffie Darrell,
Zariphopoulou Thaleia
Publication year - 1993
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1993.tb00083.x
Subject(s) - viscosity solution , hamilton–jacobi–bellman equation , bellman equation , economics , portfolio , hamilton–jacobi equation , consumption (sociology) , mathematical economics , investment (military) , mathematics , stochastic control , order (exchange) , value (mathematics) , econometrics , optimal control , mathematical optimization , financial economics , finance , statistics , social science , sociology , politics , political science , law
This paper treats the problem of consumption and portfolio choice in continuous time, with stochastic income that cannot be replicated by trading the available securities. the optimal controls and value functions are characterized in terms of the viscosity solution of the associated Hamilton‐Jacobi‐Bellman equation, which is shown to exist and is characterized. the optimal policy is then given from the first‐order conditions of the Hamilton‐Jacobi‐Bellman equation.