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Optimal portfolios in commodity futures markets. (English) Zbl 1305.91213
This paper deals with optimal portfolios in commodity markets. The authors propose a general mathematical framework for portfolio optimization on futures markets based on the Heath-Jarrow-Morton approach. In the portfolio optimization problem, the agent invests in futures contracts and a risk-free asset, and her objective is to maximize the utility from final wealth. It is studied this optimization problem in the case when the underlying price dynamics admit a finite-dimensional realization. The authors obtain conditions under which a given infinite-dimensional portfolio optimization problem can be solved in terms of a finite-dimensional control problem. Some economic interpretations of the coordinate process are analyzed, and how a solution of the finite-dimensional control problem can be connected to the coordinate process and, consequently, back to the infinite-dimensional portfolio problem. The authors obtain the Hamilton-Jacobi-Bellman equation for the finite-dimensional portfolio optimization problem and establish a verification theorem.

91G10 Portfolio theory
49N90 Applications of optimal control and differential games
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
91G20 Derivative securities (option pricing, hedging, etc.)
Full Text: DOI arXiv
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