Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Exploratory Optimal Stopping: A Singular Control Formulation

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker’s control is represented by the probability of stopping within a given time-

Lab Rats Math 9.5 Rigor 3.5 ·  August 18, 2024

On a Merton Problem with Irreversible Healthcare Investment

We propose a tractable dynamic framework for the joint determination of optimal consumption, portfolio choice, and healthcare irreversible investment. Our model is based on a Merton’s portfolio and consumption problem, where, in addition, the agent can choose the time at which undertaking a costly l

Lab Rats Math 8.5 Rigor 3 ·  December 10, 2022

Cooperation, Correlation and Competition in Ergodic N-player Games and Mean-field Games of Singular Controls: A Case Study

We consider a class of $N$-player games and mean-field games of singular controls with ergodic performance criterion, providing a benchmark case for irreversible investment games featuring mean-field interaction and strategic complementarities. The state of each player follows a geometric Brownian m

Lab Rats Math 9.2 Rigor 2.5 ·  April 23, 2024

Optimal Consumption and Portfolio Choice with No-Borrowing Constraint in the Kim-Omberg Model: The Complete Market Case

In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg model, the stochastic factor represents the expected excess re

Lab Rats Math 8.5 Rigor 2.5 ·  March 3, 2026

A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy

We consider a mean-field model of firms competing à la Cournot on a commodity market, where the commodity price is given in terms of a power inverse demand function of the industry-aggregate production. Investment is irreversible and production capacity depreciates at a constant rate. Production is

Lab Rats Math 8.5 Rigor 2.5 ·  April 30, 2023

A Stationary Equilibrium Model of Green Technology Adoption with Endogenous Carbon Price

This paper proposes and analyzes a stationary equilibrium model for a competitive industry which endogenously determines the carbon price necessary to achieve a given emission target. In the model, firms are identified by their level of technology and make production, entry, and abatement decisions.

Lab Rats Math 8 Rigor 2.5 ·  February 26, 2024

Singular Control in a Cash Management Model with Ambiguity

We consider a singular control model of cash reserve management, driven by a diffusion under ambiguity. The manager is assumed to have maxmin preferences over a set of priors characterized by $κ$-ignorance. A verification theorem is established to determine the firm’s cost function and the optimal c

Lab Rats Math 8.5 Rigor 2 ·  September 21, 2023

On the Singular Control of a Diffusion and Its Running Infimum or Supremum

We study a class of singular stochastic control problems for a one-dimensional diffusion $X$ in which the performance criterion to be optimised depends explicitly on the running infimum $I$ (or supremum $S$) of the controlled process. We introduce two novel integral operators that are consistent wit

Lab Rats Math 8.5 Rigor 1.5 ·  January 29, 2025

Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise

We study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui’s representation problem. Under certain continuity assumptions, where the common noise is generated by a countable partition, we show that a strong randomized mea

Lab Rats Math 9 Rigor 1 ·  July 25, 2025

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