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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.

MSC:
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.)
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