Related papers: Impulse Control of Multidimensional Jump Diffusion…
We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family…
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.…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…
We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition…
We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional L\'evy process. We set up a valuation model in…
We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro-differential equations. Conditions are provided under which preservation of convexity…
We prove a maximum principle for the problem of optimal control for a fractional diffusion with infinite horizon. Further, we show existence of fractional backward stochastic differential equations on infinite horizon. We illustrate our…
A fairly reliable trend in deep reinforcement learning is that the performance scales with the number of parameters, provided a complimentary scaling in amount of training data. As the appetite for large models increases, it is imperative…
In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is…
In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…
This paper examines impulsive controls related to nonautonomous impulsive integro-differential equations in Hilbert space, highlighting their significance. We establish the existence of the mild solution by using fixed point approach and…
In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case…
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
In the paper "Dynkin Games Via Dirichlet Forms and Singular Control of One-Dimensional Diffusion", the authors tried to show the existences of a smooth value function and an optimal policy to a one-dimensional stochastic singular control…
We study a class of singular stochastic control problems for a one-dimensional diffusion $X$ in which the performance criterion to be optimised depends explicitly on the running infimum $I$ (or supremum $S$) of the controlled process. We…
This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated…
We consider the diffusive limit of a typical pure-jump Markovian control problem as the intensity of the driving Poisson process tends to infinity. We show that the convergence speed is provided by the H\"older constant of the Hessian of…
We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity.…
In this article, we prove the existence of optimal risk-sensitive control with state constraints. We use near monotone assumption on the running cost to prove the existence of optimal risk-sensitive control.