Related papers: Utility maximization with random horizon: a BSDE a…
In this paper, we study an infinite horizon non-autonomous stochastic recursive differential game. To this end, we first establish well-posedness and stability results for BSDEs with a time-dependent discount factor and a possibly unbounded…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our…
We study the expected utility maximization problem of a large investor who is allowed to make transactions on tradable assets in an incomplete financial market with endogenous permanent market impacts. The asset prices are assumed to follow…
We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize…
In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncertain local characteristics. Here, the differential…
This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has…
We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one…
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed on strategies. The optimal consumption and investment…
In this work, we study the problem of mean-variance hedging with a random horizon T ^ tau, where T is a deterministic constant and is a jump time of the underlying asset price process. We rst formulate this problem as a stochastic control…
We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption…
This paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellman (HJB) equation.…
We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +$\infty$ with positive probability. We deal with equations on a general filtered probability space…
In this paper we extend the stability results of [4]}. Our utility maximization problem is defined as an essential supremum of conditional expectations of the terminal values of wealth processes, conditioned on the filtration at the…
In this article we consider risk-sensitive control of semi-Markov processes with a discrete state space. We consider general utility functions and discounted cost in the optimization criteria. We consider random finite horizon and infinite…
We develop a necessary stochastic maximum principle for a finite-dimensional stochastic control problem in infinite horizon under a polynomial growth and joint monotonicity assumption on the coefficients. The second assumption generalizes…
The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The…
We establish sufficient conditions for the existence and uniqueness of different types of delayed BSDEs in finite time horizon. We consider then infinite horizon, replacing the terminal value condition in the finite horizon case with a…
In this paper we study one dimensional backward stochastic differential equations (BSDEs) with random terminal time not necessarily bounded or finite when the generator F(t,Y,Z) has a quadratic growth in Z. We provide existence and…