Related papers: Robust Multiple Stopping -- A Pathwise Duality App…
The ability to deal with systems parametric uncertainties is an essential issue for heavy self-driving vehicles in unconfined environments. In this sense, robust controllers prove to be efficient for autonomous navigation. However,…
We study an optimal stopping problem with an unbounded, time-dependent and discontinuous reward function. This problem is motivated by the pricing of a variable annuity contract with guaranteed minimum maturity benefit, under the assumption…
We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, the causal and bicausal barycenter problem, and a…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
We study approaches to robust model-based design of experiments in the context of maximum-likelihood estimation. These approaches provide robustification of model-based methodologies for the design of optimal experiments by accounting for…
This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
This paper presents the benefits of using randomized neural networks instead of standard basis functions or deep neural networks to approximate the solutions of optimal stopping problems. The key idea is to use neural networks, where the…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite…
We study a mathematical model motivated by the support/resistance line method in technical analysis where the underlying stock price transitions between three states of nature in a path-dependent manner. For optimal stopping problems with…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
We propose an alternative approach for solving a number of well-studied optimal stopping problems for L\'evy processes. Instead of the usual method of guess-and-verify based on martingale properties of the value function, we suggest a more…
Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some…
We introduce a new method, stepwise method for solving optimal con- trol problems. Our first motivation for new approach emanate from limi- tations on continuous time control functions in PMP. Practically in most of the real world models,…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…