Optimal portfolios in commodity futures markets
Journal article, Peer reviewed
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- SAM - Handelshøyskolen 
Original versionBenth, F. E., & Lempa, J. (2014). Optimal portfolios in commodity futures markets. Finance and Stochastics, 18(2), 407-430. http://dx.doi.org/10.1007/s00780-013-0224-5
We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios of futures contracts. 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. In order to capture self-consistent futures price dynamics, we study a class of futures price curve models which admit a finite-dimensional realization. More precisely, we establish conditions under which the futures price dynamics can be realized in finite dimensions. Using the finite-dimensional realization, we derive a finite-dimensional form of the portfolio optimization problem and study its solution. We also give an economic interpretation of the coordinate process driving the finite-dimensional realization.