Related papers: On the Stability of Utility Maximization Problems
In this work we study the continuous time exponential utility maximization problem in the framework of an investor who is informed about the price changes with a delay. This leads to a non-Markovian stochastic control problem. In the case…
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…
Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the…
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by…
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 studies an $\alpha$-robust utility maximization problem where an investor faces an intractable claim -- an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case,…
In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of --…
We treat utility maximization from terminal wealth for an agent with utility function $U:\mathbb{R}\to\mathbb{R}$ who dynamically invests in a continuous-time financial market and receives a possibly unbounded random endowment. We prove the…
We study a general robust utility maximization problem in a discrete-time frictionless market. The investor is assumed to have a possibly infinite, random, nonconcave, and nondecreasing utility function defined on the whole real line. She…
The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as…
This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs, in which the commonly used concavification principle for terminal value is no longer applicable. We…
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…
We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage…
We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
In this paper the robust utility maximization problem for a market model based on L\'evy processes is analyzed. The interplay between the form of the utility function and the penalization function required to have a well posed problem is…
We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value…