Related papers: Duality Theory for Exponential Utility--Based Hedg…
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices…
We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the…
This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility…
This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is…
The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in…
This paper discusses the num\'eraire-based utility maximization problem in markets with proportional transaction costs. In particular, the investor is required to liquidate all her position in stock at the terminal time. We first observe…
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 consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the…
We consider the robust utility maximization using a static holding in derivatives and a dynamic holding in the stock. There is no fixed model for the price of the stock but we consider a set of probability measures (models) which are not…
We calculate explicitly the optimal strategy for an investor with exponential utility function when the stock price follows an autoregressive Gaussian process. We also calculate its performance and analyse it when the trading horizon tends…
We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if 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 consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by…
We consider expected utility maximisation problem for exponential Levy models and HARA utilities in presence of illiquid asset in portfolio. This illiquid asset is modelled by an option of European type on another risky asset which is…
In this paper we study optimal investment when the investor can peek some time units into the future, but cannot fully take advantage of this knowledge because of quadratic transaction costs. In the Bachelier setting with exponential…
We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, 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 present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor's preferences are represented by a multivariate utility function, allowing for…
We consider utility maximization problem for semi-martingale models depending on a random factor $\xi$. We reduce initial maximization problem to the conditional one, given $\xi=u$, which we solve using dual approach. For HARA utilities we…
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…