Related papers: One-sided solutions for optimal stopping problems …
The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process Xt and on its supremum Xt := sup 0$\le$s$\le$t Xs.…
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
We study the optimal stopping problem for dynamic risk measures represented by Backward Stochastic Differential Equations (BSDEs) with jumps and its relation with reflected BSDEs (RBSDEs). We first provide general existence, uniqueness and…
We consider an optimal stopping time problem related with many models found in real options problems. The main goal of this work is to bring for the field of real options, different and more realistic pay-off functions, and negative…
In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…
In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…
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…
Constrained optimization with multiple functional inequality constraints has significant applications in machine learning. This paper examines a crucial subset of such problems where both the objective and constraint functions are weakly…
Let Z be a strictly a-stable real Levy process (a>1) and X be a fluctuating b-homogeneous additive functional of Z. We investigate the asymptotics of the first passage-time of X above 1, and give a general upper bound. When Z has no…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
We characterize the existence of the $L^1$ solutions of the truncated moments problem in several real variables on unbounded supports by the existence of the maximum of certain concave Lagrangian functions. A natural regularity assumption…
Motivated by Kyprianou and Zhou (2009), Wang and Hu (2012), Avram et al. (2017), Li et al. (2017) and Wang and Zhou (2018), we consider in this paper the problem of maximizing the expected accumulated discounted tax payments of an insurance…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
In this paper we consider discrete and continuous time risk sensitive optimal stopping problem. Using suitable properties of the underlying Feller-Markov process we prove continuity of the optimal stopping value function and provide formula…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
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,…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…