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Optimal investment and consumption for Ornstein-Uhlenbeck spread financial markets with logarithmic utility

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  • Sahar Albosaily
  • Serguei Pergamenshchikov

Abstract

We consider a spread financial market defined by the multidimensional Ornstein--Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions in the base of stochastic dynamical programming method. We show a special Verification Theorem for this case. We find the solution to the Hamilton--Jacobi--Bellman (HJB) equation in explicit form and as a consequence we construct the optimal financial strategies. Moreover, we study the constructed strategy by numerical simulations.

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  • Sahar Albosaily & Serguei Pergamenshchikov, 2018. "Optimal investment and consumption for Ornstein-Uhlenbeck spread financial markets with logarithmic utility," Papers 1809.08139, arXiv.org.
    • Handle: RePEc:arx:papers:1809.08139
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