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In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic backward equation under the worst-case scenario. In a time-homogeneous setting - where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called k-ignorance - we are able to provide the explicit form of the optimal irreversible investment plan.
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity a
We investigate the optimal portfolio deleveraging (OPD) problem with permanent and temporary price impacts, where the objective is to maximize equity while meeting a prescribed debt/equity requirement. We take the real situation with cross impact amo
This paper studies the retirement decision, optimal investment and consumption strategies under habit persistence for an agent with the opportunity to design the retirement time. The optimization problem is formulated as an interconnected optimal sto
This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis to compare
We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invest