Opuscula Math. 35, no. 4 (2015), 547-560

Opuscula Mathematica

Optimal consumption problem in the Vasicek model

Jakub Trybuła

Abstract. We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumption strategy and the value function.

Keywords: stochastic control, interest rate model, optimal consumption, HJB equation.

Mathematics Subject Classification: 93E20, 60H30.

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  • Jakub Trybuła
  • Cracow University of Economics, Department of Mathematics, Rakowicka 27, 31-510 Kraków, Poland
  • Received: 2013-10-10.
  • Revised: 2014-11-03.
  • Accepted: 2014-11-03.
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Cite this article as:
Jakub Trybuła, Optimal consumption problem in the Vasicek model, Opuscula Math. 35, no. 4 (2015), 547-560, http://dx.doi.org/10.7494/OpMath.2015.35.4.547

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