TL;DR
This paper develops a model for optimal dynamic trading of futures and underlying assets using a stochastic basis modeled by a stopped scaled Brownian bridge, deriving explicit strategies under HARA preferences.
Contribution
It introduces a novel stochastic basis model and explicitly solves the utility maximization problem for dynamic trading strategies.
Findings
Explicit solutions for optimal trading strategies.
Conditions for the existence of solutions to the HJB equation.
Numerical illustrations of strategy performance and parameter effects.
Abstract
We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a utility maximization problem under hyperbolic absolute risk aversion (HARA) risk preferences. By analyzing the associated Hamilton-Jacobi-Bellman equation, we derive the exact conditions under which the equation admits a solution and solve the utility maximization explicitly. A series of numerical examples are provided to illustrate the optimal strategies and examine the effects of model parameters.
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