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Constrained dynamic futures portfolios with stochastic basis

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Abstract

We study the problem of dynamically trading multiple futures contracts on different underlying assets subject to portfolio constraints. The spreads between futures and spot prices are modeled by a multidimensional scaled Brownian bridge to account for their convergence at maturity. Under this stochastic basis model, we apply the stochastic control approach to rigorously derive the optimal trading strategies via utility maximization. This leads to the analysis of the associated system of Hamilton-Jacobi-Bellman equations, which are reduced to a system of ODEs. A series of numerical examples are provided to illustrate the optimal strategies and wealth distributions under different portfolio constraints.

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Xiaodong Chen

  2. Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, USA

    Tim Leung & Yang Zhou

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  1. Xiaodong Chen
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  2. Tim Leung
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  3. Yang Zhou
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Correspondence to Tim Leung.

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Chen, X., Leung, T. & Zhou, Y. Constrained dynamic futures portfolios with stochastic basis. Ann Finance 18, 1–33 (2022). https://doi.org/10.1007/s10436-021-00398-0

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