Related papers: Utility maximization via decoupling fields
We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns…
Building on previous work on the stochastic analysis for Grassmann random variables, we introduce a forward-backward stochastic differential equation (FBSDE) which provides a stochastic quantisation of Grassmann measures. Our method is…
Network utility maximization is the most important problem in network traffic management. Given the growth of modern communication networks, we consider the utility maximization problem in a network with a large number of connections…
Benchmarks in the utility function have various interpretations, including performance guarantees and risk constraints in fund contracts and reference levels in cumulative prospect theory. In most literature, benchmarks are a deterministic…
Managing power grids with the increasing presence of variable renewable energy-based (distributed) generation involves solving high-dimensional optimization tasks at short intervals. Linearizing the AC power flow (PF) constraints is a…
This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the standard setting, a possibly non-concave utility…
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 solve the Skorokhod embedding problem for a class of Gaussian processes including Brownian motion with non-linear drift. Our approach relies on solving an associated strongly coupled system of Forward Backward Stochastic Differential…
We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance…
In this paper, we study a maximization problem on real sequences. More precisely, for a given sequence, we are interested in computing the supremum of the sequence and an index for which the associated term is maximal. We propose a general…
In this paper we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality…
We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees,…
We consider an online version of the well-studied network utility maximization problem, where users arrive one by one and an operator makes irrevocable decisions for each user without knowing the details of future arrivals. We propose a…
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 make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic…
Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate…
In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical data and the information on the true utility function is incomplete. To mitigate…
This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different…
The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial…
This paper concerns the recursive utility maximization problem. We assume that the coefficients of the wealth equation and the recursive utility are concave. Then some interesting and important cases with nonlinear and nonsmooth…