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We consider the problem of optimally stopping a Brownian bridge with an unknown pinning time so as to maximise the value of the process upon stopping. Adopting a Bayesian approach, we assume the stopper has a general continuous prior and is…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
Autonomous crypto trading systems often spend most of their design effort on finding entries, while exits are left to fixed rules that are rarely tested in a systematic way. This paper examines whether better stop-loss and take-profit…
In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not…
Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject…
Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For…
We consider risk averse investors with different levels of anxiety about asset price drawdowns. The latter is defined as the distance of the current price away from its best performance since inception. These drawdowns can increase either…
We consider a manufacturer who manages the end-of-life phase and takes one of the three actions at each period: (1) place an order, (2) use existing inventory, (3) stop holding inventory and use an outside/alternative source. Two examples…
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on…
Reliable automated driving technology is challenged by various sources of uncertainties, in particular, behavioral uncertainties of traffic agents. It is common for traffic agents to have intentions that are unknown to others, leaving an…
Aiming to analyze the impact of environmental transition on the value of assets and on asset stranding, we study optimal stopping and divestment timing decisions for an economic agent whose future revenues depend on the realization of a…
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We…
We study the problem of selling an asset near its ultimate maximum in the minimax setting. The regret-based notion of a perfect stopping time is introduced. A perfect stopping time is uniquely characterized by its optimality properties and…
In this work we study the optimal execution problem with multiplicative price impact in algorithm trading, when an agent holds an initial position of shares of a financial asset. The inter-selling-decision times are modelled by the arrival…
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…
Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…
A principal hires an agent to work on a long-term project that culminates in a breakthrough or a breakdown. At each time, the agent privately chooses to work or shirk. Working increases the arrival rate of breakthroughs and decreases the…
Most modern control systems are switched, meaning they have continuous as well as discrete decision variables. Switched systems often have constraints called dwell-time constraints (e.g., cycling constraints in a heat pump) on the switching…
We study a class of infinite-horizon impulse control problems with execution delay in discrete time. Using probabilistic methods, particularly the notion of the Snell envelope of processes, we construct an optimal strategy among all…
Stop-loss rules are often studied in the financial literature, but the stop-loss levels are seldom constructed systematically. In many papers, and indeed in practice as well, the level of the stops is too often set arbitrarily. Guided by…