Related papers: Limit value for optimal control with general means
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…
De Finetti's optimal reinsurance is a set of contracts, one for each risk in a portfolio, that caps the retained aggregate variance to a pre-specified level while minimizing total expected loss. The premiums are determined using the…
A class of infinite horizon optimal control problems involving $L^p$-type cost functionals with $0<p\leq 1$ is discussed. The existence of optimal controls is studied for both the convex case with $p=1$ and the nonconvex case with $0<p<1$,…
We establish a general framework that guarantees the preservation of optimal control patterns as the time horizon $[0,T]$ increases and becomes unbounded. A concept of pattern-preserving family of optimal control problems is introduced and…
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…
We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterise the value function via HJB equation…
In an optimal control strategy, an important point is to define the cost of the control. Usually it is added to the control criterion and multiplied by a small coefficient denoted by $\varepsilon$ which is known as the marginal cost of the…
We analyze the limiting behavior of the risk premium associated with the Pareto optimal risk sharing contract in an infinitely expanding pool of risks under a general class of law-invariant risk measures encompassing rank-dependent utility…
Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome…
This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we…
We study statistical properties of the optimal value of the Sample Average Approximation. The focus is on the tail function of the absolute error induced by the Sample Average Approximation, deriving upper estimates of its outcomes…
This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…
In this paper, we consider the concept of limit, one of the basic concepts of mathematical analysis. At a point $a\in{\mathbb{R}}$, the limit of a function $f$ from $A\subset\mathbb{R}$ to $\mathbb{R}$ is $L\in{\mathbb{R}}$ if and only if…
Motivated by applications in natural resource management, risk management, and finance, this paper is focused on an ergodic two-sided singular control problem for a general one-dimensional diffusion process. The control is given by a…
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions…
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some…
This paper investigates the necessary optimality conditions for uniformly overtaking optimal control on infinite horizon in the free end case. %with free right endpoint. In the papers of S.M.Aseev, A.V.Kryazhimskii, V.M.Veliov, K.O.Besov…