Optimal portfolio management rules in a non-Gaussian market with durability and intertemporal substitution
| Autor: | Kristin Reikvam, Kenneth H. Karlsen, Fred Espen Benth |
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| Rok vydání: | 2001 |
| Předmět: |
Statistics and Probability
Stochastic control jel:D91 Mathematical optimization Optimization problem Mathematical finance jel:C61 Lévy process Singular control jel:G11 Portfolio choice intertemporal substitution singular stochastic control dynamic programming method integro-differential variational inequality viscosity solution closed form solution Bellman equation Statistics Probability and Uncertainty Special case Viscosity solution Finance Mathematics |
| Popis: | We consider an optimal portfolio-consumption problem which incorporates the notions of durability and intertemporal substitution. The logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve Levy processes as driving noise instead of the more frequently used Brownian motion. The optimization problem is a singular stochastic control problem and the associated Hamilton-Jacobi-Bellman equation is a nonlinear second order degenerate elliptic integro-differential equation subject to gradient and state constraints. For utility functions of HARA type, we calculate the optimal investment and consumption policies together with an explicit expression for the value function when the Levy process has only negative jumps. For the classical Merton problem, which is a special case of our optimization problem, we provide explicit policies for general Levy processes having both positive and negative jumps. Instead of following the classical approach of using a verification theorem, we validate our solution candidates within a viscosity solution framework. To this end, the value function of our singular control problem is characterized as the unique constrained viscosity solution of the Hamilton-Jacobi-Bellman equation in the case of general utilities and general Levy processes. |
| Databáze: | OpenAIRE |
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