Related papers: Utility Maximization under Model Uncertainty in Di…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
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…
This paper studies the problem of maximizing expected utility from terminal wealth combining a static position in derivative securities, which we assume can be traded only at time zero, with a traditional dynamic trading strategy in stocks.…
In this work we study a continuous time exponential utility maximization problem in the presence of a linear temporary price impact. More precisely, for the case where the risky asset is given by the Ornstein-Uhlenbeck diffusion process we…
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two…
Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an…
This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…
We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for existence and uniqueness of the solution and give a characterization…
One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…
This paper proposes two approaches that quantify the exact relationship among the viability, the absence of arbitrage, and/or the existence of the num\'eraire portfolio under minimal assumptions and for general continuous-time market…
In this paper we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfect strategies with the adaptive robust stochastic to tackle…
We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization…
We consider a problem of optimal investment with intermediate consumption in the framework of an incomplete semimartingale model of a financial market. We show that a necessary and sufficient condition for the validity of key assertions of…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
We pursue an inverse approach to utility theory and consumption & investment problems. Instead of specifying an agent's utility function and deriving her actions, we assume we observe her actions (i.e. her consumption and investment…
We establish the existence and characterization of a primal and a dual facelift - discontinuity of the value function at the terminal time - for utility-maximization in incomplete semimartingale-driven financial markets. Unlike in the…
The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker's preferences. In order to obtain such utility values it is necessary to establish an analogy between…
In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $\xi$ in a risk-conservative way relative…
We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari's dual theory of choice and quantile maximization as special cases. We characterize when the optimal…
Management of a portfolio that includes an illiquid asset is an important problem of modern mathematical finance. One of the ways to model illiquidity among others is to build an optimization problem and assume that one of the assets in a…