Related papers: Optimal Stopping for Non-linear Expectations
We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player…
In this article we study the expected rank problem under full information. Our approach uses the planar Poisson approach from Gnedin (2007) to derive the expected rank of a stopping rule that is one of the simplest non-trivial examples…
This paper presents a continuous-time optimal control framework for the generation of reference trajectories in driving scenarios with uncertainty. A previous work presented a discrete-time stochastic generator for autonomous vehicles;…
While LLMs have seen substantial improvement in reasoning capabilities, they also sometimes overthink, generating unnecessary reasoning steps, particularly under uncertainty, given ill-posed or ambiguous queries. We introduce statistically…
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
In this paper, we investigate an optimal control problem with terminal stochastic linear complementarity constraints (SLCC), and its discrete approximation using the relaxation, the sample average approximation (SAA) and the implicit Euler…
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…
We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer.…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty.…
We propose a novel group of Gaussian Process based algorithms for fast approximate optimal stopping of time series with specific applications to financial markets. We show that structural properties commonly exhibited by financial time…
Autonomous control systems use various sensors to decrease the amount of uncertainty under which they operate. While providing partial observation of the current state of the system, sensors require resources such as energy, time and…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
We introduce discontinuous solutions to nonlinear impulsive control systems with state time delays in the dynamics and derive necessary optimality conditions in the form of a Maximum Principle for associated optimal control problems. In the…
A novel quickest detection setting is proposed which is a generalization of the well-known Bayesian change-point detection model. Suppose \{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S is a stopping time with…
The paper addresses the problem of computing maximal conditional expected accumulated rewards until reaching a target state (briefly called maximal conditional expectations) in finite-state Markov decision processes where the condition is…
We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…
We study optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values…
In this paper we provide a theoretical analysis of Variable Annuities with a focus on the holder's right to an early termination of the contract. We obtain a rigorous pricing formula and the optimal exercise boundary for the surrender…