Related papers: Utility maximization via decoupling fields
In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward…
We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with…
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 study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an $R^d$-valued continuous…
Connections between a system of Forward-Backward SDEs and Backward Stochastic PDEs related to the utility maximiza- tion problem is established. Besides, we derive another version of FBSDE of the same problem and prove an existence of a…
In this paper, we consider the classical problem of utility maximization in a financial market allowing jumps. Assuming that the constraint set is a compact set, rather than a convex one, we use a dynamic method from which we derive a…
This paper studies the utility maximization problem of an agent with non-trivial endowment, and whose preferences are modeled by the maximal subsolution of a BSDE. We prove existence of an optimal trading strategy and relate our existence…
In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness…
This paper investigates an optimal consumption-investment problem featuring recursive utility via Tsallis relative entropy. We establish a fundamental connection between this optimization problem and a quadratic backward stochastic…
We consider the problem of utility maximization with exponential preferences in a market where the traded stock/risky asset price is modelled as a L\'evy-driven pure jump process (i.e. the driving L\'evy process has no Brownian component).…
We develop an existence, uniqueness and regularity theory for general multidimensional strongly coupled FBSDE using so called decoupling fields. We begin with a local result and extend it to a global theory via concatenation. The…
We study a robust utility maximization problem in the case of an incomplete market and logarithmic utility with general stochastic constraints, not necessarily convex. Our problem is equivalent to maximizing of nonlinear expected…
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic…
We study a robust utility maximization problem in the unbounded case with a general penalty term and information including jumps. We focus on time consistent penalties and we prove that there exists an optimal probability measure solution…
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic…
In this paper, we study a class of real-valued mean-field backward stochastic differential equations (BSDEs) with generators of quadratic growth in the control variable and the mean-field term. Under this assumption, together with a bounded…
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.…
This paper studies finite-time optimal consumption-investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients, subject to coupled constraints on the consumption and…
In this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific BSDE, which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We…