Related papers: Backward Stochastic PDEs related to the utility ma…
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…
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…
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 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…
This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend…
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).…
This article studies the problem of utility maximization in an incomplete market under a class of nonlinear expectations and general constraints on trading strategies. Using a $g$-martingale method, we provide an explicit solution to our…
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 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 consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for…
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…
We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem,…
In this paper, we study the classical problem of maximization of the sum of the utility of the terminal wealth and the utility of the consumption, in a case where a sudden jump in the risk-free interest rate creates incompleteness. The…
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…
We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization…
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 perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected…
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…
We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility.…