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Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when…
Oscillatory flow patterns have been observed in many different driven many-particle systems. The conventional assumption is that the reason for emergent oscillations in opposing flows is an increased efficiency (throughput). In this…
We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…
We study the optimal investment policy of a firm facing both technological and cash-flow uncertainty. At any point in time, the firm can decide to invest in a standalone technology or to wait for a technological breakthrough. Breakthroughs…
A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon.…
Continuous optimization based motion planners require specifying a maneuver class before calculating the optimal trajectory for that class. In traffic, the intentions of other participants are often unclear, presenting multiple maneuver…
Motivated by the cost savings that can be obtained by sharing resources in a network context, we consider a stylized, yet representative model, for the coordination of maintenance and service logistics for a geographic network of assets.…
In this paper, we solve the time inconsistent portfolio selection problem by using different utility functions with a moving target as our constraint. We solve this problem by finding an equilibrium control under the given definition as our…
In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium…
We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a…
We study the tradeoff between fundamental risk and time. A time-constrained agent has to solve a problem. She dynamically allocates effort between implementing a risky initial idea and exploring alternatives. Discovering an alternative…
This paper discusses a nonlinear integral equation arising from portfolio selection with a class of time-inconsistent preferences. We propose a unified framework requiring minimal assumptions, such as right-continuity of market coefficients…
Commodity futures constitute an attractive asset class for portfolio managers. Propelled by their low correlation with other assets, commodities begin gaining popularity among investors, as they allow to capture diversification benefits.…
In behavioral economics, human decision makers are modeled as anticipatory agents that make decisions by taking into account the probability of future decisions (plans). We consider cyber-physical systems involving the interaction between…
This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost…
A decision maker repeatedly chooses one of a finite set of actions. In each period, the decision maker's payoff depends on fixed basic payoff of the chosen action and the frequency with which the action has been chosen in the past. We…
In this paper, we study a continuous-time discounted jump Markov decision process with both controlled actions and observations. The observation is only available for a discrete set of time instances. At each time of observation, one has to…
This paper studies relations among axioms on individuals' intertemporal choices under risk. The focus is on Risk Averse over Time Lotteries (RATL), meaning that a fixed prize is preferred to a lottery with the same monetary prize but a…