Related papers: Utility maximization with random horizon: a BSDE a…
Necessary optimality conditions in the form of the maximum principle for control problems with infinite time horizon are considered. Both finite and infinite values of objective functional are allowed since the concept of overtaking or…
We consider a classical finite horizon optimal control problem for continuous-time pure jump Markov processes described by means of a rate transition measure depending on a control parameter and controlled by a feedback law. For this class…
We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that…
In this paper, we study the existence of solution to BSDE with quadratic growth and unbounded terminal value. We apply a localization procedure together with a priori bounds. As a byproduct, we apply the same method to extend a result on…
In this paper we study the optimal m-states switching problem in finite horizon as well as infinite horizon with risk of default. We allow the switching cost functionals and cost of default to be of polynomial growth and arbitrary. We show…
Multi-hop random access networks have received much attention due to their distributed nature which facilitates deploying many new applications over the sensor and computer networks. Recently, utility maximization framework is applied in…
In this paper, we study optimal liquidation problems in a randomly-terminated horizon. We consider the liquidation of a large single-asset portfolio with the aim of minimizing a combination of volatility risk and transaction costs arising…
Infinite horizon optimization problems accompany two perplexities. First, the infinite series of utility sequences may diverge. Second, boundary conditions at the infinite terminal time may not be rigorously expressed. In this paper, we…
In this paper, we propose a method for bounding the probability that a stochastic differential equation (SDE) system violates a safety specification over the infinite time horizon. SDEs are mathematical models of stochastic processes that…
Submodular function maximization is a fundamental combinatorial optimization problem with plenty of applications -- including data summarization, influence maximization, and recommendation. In many of these problems, the goal is to find a…
We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real…
We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of…
Multi-hop random access networks have received much attention due to their distributed nature which facilitates deploying many new applications over the sensor and computer networks. Recently, utility maximization framework is applied in…
In this paper we investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black-Scholes type financial market which may be incomplete. We impose a constraint on the admissible strategies that…
This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We…
In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual…
We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…
The existence of optimal strategy in robust utility maximization is addressed when the utility function is finite on the entire real line. A delicate problem in this case is to find a "good definition" of admissible strategies, so that an…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…