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Optimal portfolios in commodity futures markets

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  • Fred Benth
  • Jukka Lempa

Abstract

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Fred Benth & Jukka Lempa, 2014. "Optimal portfolios in commodity futures markets," Finance and Stochastics, Springer, vol. 18(2), pages 407-430, April.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:2:p:407-430
    DOI: 10.1007/s00780-013-0224-5
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    10. Benth, Fred Espen & Cartea, Álvaro & Kiesel, Rüdiger, 2008. "Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2006-2021, October.
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    Citations

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    Cited by:

    1. Fred Espen Benth & Paul Krühner, 2018. "Approximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models," Finance and Stochastics, Springer, vol. 22(2), pages 327-366, April.
    2. Fred Espen Benth & Paul Kruhner, 2015. "Approximation of forward curve models in commodity markets with arbitrage-free finite dimensional models," Papers 1512.05983, arXiv.org.
    3. Benth, Fred Espen & Paraschiv, Florentina, 2016. "A Structural Model for Electricity Forward Prices," Working Papers on Finance 1611, University of St. Gallen, School of Finance.
    4. Fred Espen Benth & Paul Kruhner, 2014. "Derivatives pricing in energy markets: an infinite dimensional approach," Papers 1412.7943, arXiv.org.
    5. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    6. Charles Shaw, 2022. "Portfolio Diversification Revisited," Papers 2204.13398, arXiv.org.
    7. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    8. Junhe Chen & Marcos Escobar-Anel, 2021. "Model uncertainty on commodity portfolios, the role of convenience yield," Annals of Finance, Springer, vol. 17(4), pages 501-528, December.

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    More about this item

    Keywords

    Futures contract; Commodity markets; Optimal portfolios; Stochastic partial differential equations; Finite-dimensional realization; Invariant foliation; 91G10; 60H15; G11; G13; C61;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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