Related papers: The Merton Problem with a Drawdown Constraint on C…
We study merchant energy production modeled as a compound switching and timing option. The resulting Markov decision process is intractable. State-of-the-art approximate dynamic programming methods applied to realistic instances of this…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
We prove a verification theorem for a class of singular control problems which model optimal harvesting with density-dependent prices or optimal dividend policy with capital-dependent utilities. The result is applied to solve explicitly…
We consider an online revenue maximization problem over a finite time horizon subject to lower and upper bounds on cost. At each period, an agent receives a context vector sampled i.i.d. from an unknown distribution and needs to make a…
Assortment optimization concerns the problem of selling items with fixed prices to a buyer who will purchase at most one. Typically, retailers select a subset of items, corresponding to an "assortment" of brands to carry, and make each…
We consider a Markov control model in discrete time with countable both state space and action space. Using the value function of a suitable long-run average reward problem, we study various reachability/controllability problems. First, we…
While learning in an unknown Markov Decision Process (MDP), an agent should trade off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward. Although the agent will…
In this article we study a multi-asset version of the Merton investment and consumption problem with proportional transaction costs. In general it is difficult to make analytical progress towards a solution in such problems, but we…
The paper proposes a new stochastic intervention control model conducted in various commodity and stock markets. The essence of the phenomenon of intervention is described in accordance with current economic theory. A review of papers on…
The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
I study the optimal allocation of positional goods in the presence of externalities arising from consumers' concerns about relative consumption. Applications include luxury goods, priority services, education, and organizational…
Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is…
In this paper, we study a new stochastic submodular maximization problem with state-dependent costs and rejections. The input of our problem is a budget constraint $B$, and a set of items whose states (i.e., the marginal contribution and…
It is shown that the dual to the linear programming problem that arises in constraint-based models of metabolism can be given a thermodynamic interpretation in which the shadow prices are chemical potential analogues, and the objective is…
This paper revisits the classic instrument choice problem in a setting with consumption externalities, through the lens of robust mechanism design. A regulator can implement any incentive-compatible policy but is uncertain about how…
We consider an irreversible investment problem under incomplete information, where the investor decides whether and when to make investments in a project. Upon investment, the investor acquires previously hidden information from the…
We consider the Merton problem of optimizing expected power utility of terminal wealth in the case of an unobservable Markov-modulated drift. What makes the model special is that the agent is allowed to purchase costly expert opinions of…
Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which…