Related papers: Convex duality for stochastic differential utility
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are…
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…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…
We revisit Merton's portfolio optimization problem under boun-ded state-dependent utility functions, in a market driven by a L\'evy process $Z$ extending results by Karatzas et. al. (1991) and Kunita (2003). The problem is solved using a…
We consider an expected utility maximization problem where the utility function is not necessarily concave and the time horizon is uncertain. We establish a necessary and sufficient condition for the optimality for general non-concave…
We investigate expected utility maximization problems from the terminal liquidation value in continuous time in markets with transaction costs and one fixed consistent price system, where a non-concave utility function is defined on the…
We consider a financial market with a stock exposed to a counterparty risk inducing a drop in the price, and which can still be traded after this default time. We use a default-density modeling approach, and address in this incomplete…
We adress the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where the price process of risky assets can have a default time. Using dynamic…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
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…
In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a \textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly…
In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676--713], stochastic…
This paper develops a highly general convex duality framework for the perturbed utility route choice (PURC) model. We show that the traveler's constrained, potentially non-smooth utility maximization problem admits a dual formulation: an…
In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in…
We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop…