arXiv research

This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probabil…

Existence of strong randomized equilibria in mean-field games with common noise.

Extends RL to random stopping times, improving optimization.

The paper analyzes log-optimal and numéraire portfolios in market models stopped at random times.

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $δ$, the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise c…

This paper studies a class of optimal multiple stopping problems driven by Lévy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real options, where the strike price can potentially grow at a higher rate than the original d…

Improved algorithm for optimal stopping problems reduces runtime.

This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which is also known in the literature as the first kind of non-arbitrage. For this non-arbitrage notion, we ob…

The paper tackles optimal stopping problems using reinforcement learning and singular control.

Study optimal stopping in random exploration, deriving HJB and designing a reinforcement learning algorithm.

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we …

Solves optimal stopping problem with Poisson constraints using jumps.

Analyzes Lévy flights on manifolds for finding small targets.

Early stopping is a well known approach to reduce the time complexity for performing training and model selection of large scale learning machines. On the other hand, memory/space (rather than time) complexity is the main constraint in many applications, and randomized subsampling techniques have been proposed to tackl…

We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of some continuous index process at which the payoff process is even allowed to have…

Study optimal stopping times under regime-switching models with constraints.

Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to cons…

New method solves optimal stopping problems using rough path signatures.

Study on randomized algorithms for optimal stopping problems.

New method models stopping times that can be equal with non-zero probability.

New algorithms improve stopping time for best arm identification.

Randomized neural networks improve optimal stopping problems efficiently.

Given an initial (resp., terminal) probability measure $μ$ (resp., $ν$) on $\mathbb{R}^d$, we characterize those optimal stopping times $τ$ that maximize or minimize the functional $\mathbb{E} |B_0 - B_τ|^α$, $α> 0$, where $(B_t)_t$ is Brownian motion with initial law $B_0\sim μ$ and with final distribution --once stop…

We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence t…

Random matrix theory explains transient signal detectability in early-stopped gradient flow.

Optimal policy for early stopping improves black-box optimization efficiency.

New method uses neural networks for optimal stopping time problems.

Develops a model for gambling decisions under time inconsistency.

The paper studies RBSDEs with arbitrary stopping times and their solutions.

In this paper, we provide a solution to two problems which have been open in default time modeling in credit risk. We first show that if $τ$ is an arbitrary random (default) time such that its Azéma's supermartingale $Z_t^τ=¶(τ>t|\F_t)$ is continuous, then $τ$ avoids stopping times. We then disprove a conjecture about …

Gradient-flow optimization is reinterpreted as a statistical inference problem.

The paper develops formulas for hedging and arbitrage in markets with random stopping times.

Optimal exit strategies of CPT gamblers in unfair gambles

We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative Lévy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first time when the occupation time of the underlying Lévy process below a level $y$, ex…

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 to a trailing stop. Under a general linear diffusion framework, we study an opt…

This paper introduces a new class of Dynkin games, where the two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterized by the solution of a backward stochastic differential equation. The pa…

This paper completes the two studies undertaken in \cite{aksamit/choulli/deng/jeanblanc2} and \cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called NUPBR hereafter) when the stock price processes are quasi-left-continu…

This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this work is a financial or ac…

In the spirit of [Surya07'], we develop an average problem approach to prove the optimality of threshold type strategies for optimal stopping of Lévy models with a continuous additive functional (CAF) discounting. Under spectrally negative models, we specialize this in terms of conditions on the reward function and ran…

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 just on the terminal value of the fund level, but also on the lowest and the high…

Study speculative trading using RL with exploratory framework.

The paper analyzes optimal retirement timing considering age-dependent mortality risk.

Investors with anxiety about drawdowns may use stop-loss and trailing stops as optimal selling strategies.

New algorithm selects robust martingale for optimal stopping problems.

Study optimal stopping for diffusion processes with unknown primitives, applying RL and martingale methods.

This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of Aksamit/Choulli/Deng/Jeanblanc [1] in which the authors studied similar topics for the case of stopping…

Study on BSDEs with random time horizon, focusing on existence and properties.

Bayesian models predict Collatz stopping times with high accuracy.