Trading a mean-reverting asset: Buy low and sell high
Automatica (Journal of IFAC)
A trend-following strategy: Conditions for optimality
Automatica (Journal of IFAC)
Trend Following Trading under a Regime Switching Model
SIAM Journal on Financial Mathematics
Optimal Stopping in Lévy Models for Nonmonotone Discontinuous Payoffs
SIAM Journal on Control and Optimization
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We consider the problem of determining the optimal investment level that a firm should maintain in the presence of random price and/or demand fluctuations. We model market uncertainty by means of a geometric Brownian motion, and we consider general running payoff functions. Our model allows for capacity expansion as well as for capacity reduction, with each of these actions being associated with proportional costs. The resulting optimization problem takes the form of a singular stochastic control problem that we solve explicitly. We illustrate our results by means of the so-called Cobb-Douglas production function. The problem that we study presents a model in which the associated Hamilton-Jacobi-Bellman equation admits a classical solution that conforms with the underlying economic intuition but does not necessarily identify with the corresponding value function, which may be identically equal to $\infty$. Thus, our model provides a situation that highlights the need for rigorous mathematical analysis when addressing stochastic optimization applications in finance and economics, as well as in other fields.