An irreversible investment model with a stochastic production capacity and fixed plus proportional adjustment costs

This paper studies the problem of a company which expands its stochastic production capacity in irreversible investments by purchasing capital and faces both fixed and proportional costs. The objective of the company is to find optimal production decisions to maximize its expected total net profit in an infinite horizon. We solve this problem explicitly by applying the theory of stochastic impulse controls.Irreversible investment; production; quasi-variational inequalities; stochastic impulse control

Controlling the risky fraction process with an ergodic criterion

This article examines a tracking problem, similar to the one presented in Pliska and Suzuki (Quantitative Finance, 2004): an investor would keep constant proportions of her wealth in different assets if markets were frictionless; however, in the presence of fixed and proportional transaction costs her implementation problem is to keep asset proportions close to the target levels whilst avoiding too much intervention costs. Instead of minimizing discounted tracking error plus transaction costs over an infinite horizon, the optimization objective here is minimization of long run tracking error plus intervention costs per unit time. This ergodic problem is treated via combining basic tools from diffusion theory and nonlinear optimization techniques. A comparative sensitivity analysis of the ergodic and discounted problems is undertaken.

Bounded variation control of Itô diffusions with exogenously restricted intervention times

In this paper, bounded variation control of one-dimensional diffusion processes is considered. We assume that the agent is allowed to control the diffusion only at the jump times of an observable, independent Poisson process. The agent's objective is to maximize the expected present value of the cumulative payoff generated by the controlled diffusion over its lifetime. We propose a relatively weak set of assumptions on the underlying diffusion and the instantaneous payoff structure, under which we solve the problem in closed form. Moreover, we illustrate the main results with an explicit example

On the Solution of General Impulse Control Problems Using Superharmonic Functions

In this paper, a characterization of the solution of impulse control problems in terms of superharmonic functions is given. In a general Markovian framework, the value function of the impulse control problem is shown to be the minimal function in a convex set of superharmonic functions. This characterization also leads to optimal impulse control strategies and can be seen as the corresponding characterization to the description of the value function for optimal stopping problems as a smallest superharmonic majorant of the reward function. The results are illustrated with examples from different fields, including multiple stopping and optimal switching problems