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Long-term optimal investment strategies in the presence of adjustment costs
Arne Løkka,Mihail Zervos +1 more
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This work solves the genuinely two-dimensional stochastic control problem by constructing an explicit solution to an appropriate Hamilton--Jacobi--Bellman equation and by fully characterizing an optimal investment strategy.Abstract:
We consider the problem of determining in a dynamical way the optimal capacity level of an investment project that operates within a random economic environment. In particular, we consider an investment project that yields payoff at a rate that depends on its installed capacity level and on a random economic indicator such as the price of the project's output commodity. We model this economic indicator by means of a general one-dimensional ergodic diffusion. At any time, the project's capacity level can be increased or decreased at given proportional costs. The aim is to maximize an ergodic performance criterion that reflects the long-term average payoff resulting from the project's management. We solve this genuinely two-dimensional stochastic control problem by constructing an explicit solution to an appropriate Hamilton--Jacobi--Bellman equation and by fully characterizing an optimal investment strategy.read more
Citations
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Journal ArticleDOI
An optimal pairs-trading rule
Qingshuo Song,Qing Zhang +1 more
TL;DR: In this paper, a pairs trading rule is proposed to monitor two historically correlated securities and to trade the pair so as to maximize an overall return, where a fixed commission cost is charged with each transaction and a stop-loss limit is imposed as a state constraint.
Journal ArticleDOI
Irreversible Capital Accumulation with Economic Impact
Hessah Al Motairi,Mihail Zervos +1 more
TL;DR: In this article, the authors consider an irreversible capacity expansion model in which additional investment has a strictly negative effect on the value of an underlying stochastic economic indicator, and the associated optimisation problem takes the form of a singular control problem that admits an explicit solution.
Journal ArticleDOI
An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions
TL;DR: The optimal pairs-trading problem is considered by allowing the stock prices to follow general geometric Brownian motions and the objective is to trade the pairs over time to maximize an overall return with a fixed commission cost for each transaction.
Journal ArticleDOI
Optimal Exit Strategies for Investment Projects
TL;DR: In this paper, the authors studied the problem of an optimal exit strategy for an investment project which is unprofitable and for which the liquidation costs evolve stochastically, and characterized the objective function as the unique viscosity solution of the associated system of variational Hamilton-Jacobi-Bellman inequalities.
Journal ArticleDOI
Optimal exit strategies for investment projects
TL;DR: In this paper, the authors studied the problem of an optimal exit strategy for an investment project which is unprofitable and for which the liquidation costs evolve stochastically, and characterized the objective function as the unique viscosity solution of the associated system of variational Hamilton-Jacobi-Bellman inequalities.
References
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Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book
Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.
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Markov Models & Optimization
TL;DR: In this article, the authors present a new approach to problems of evaluating and optimizing the performance of continuous-time stochastic systems, based on the use of a family of Markov processes called Piecewise-Deterministic Processes (PDPs) as a general class of stocha- system models.
Journal ArticleDOI
Optimal Investment with Costly Reversibility
Andrew B. Abel,Janice C. Eberly +1 more
TL;DR: In this paper, the Jorgensonian concept of user cost of capital was extended to the case of irreversible investment and the authors defined and calculated the user costs of capital associated with the purchase and sale of capital, respectively.
Posted Content
Capacity Management, Investment, and Hedging: Review and Recent Developments
Van Mieghem,A Jan +1 more
TL;DR: This paper reviews models of capacity investment under uncertainty in three settings and reviews how to incorporate risk aversion in capacity investment and contrasts hedging strategies involving financial versus operational means.