Related papers: A unified framework for utility maximization probl…
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…
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 the general framework of a semimartingale financial model and a utility function $U$ defined on the positive real line, we compute the first-order expansion of marginal utility-based prices with respect to a ``small'' number of random…
We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a…
We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed…
We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility.…
We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization…
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 obtain variants of the classical von Neumann-Morgenstern expected utility theorem, with and without the completeness axiom, in which the derived Bernoulli utility functions are Lipschitz. The prize space in these results is an arbitrary…
Within a common arbitrage-free semimartingale financial market we consider the problem of determining all Nash equilibrium investment strategies for $n$ agents who try to maximize the expected utility of their relative wealth. The utility…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
We investigate robust Orlicz spaces as a generalisation of robust $L^p$-spaces. Two constructions of such spaces are distinguished, a top-down approach and a bottom-up approach. We show that separability of robust Orlicz spaces or their…
We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the…
A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: (i) The optimal terminal wealth $X^*(T) : = X_{\varphi^*}(T)$ of the problem to maximize the expected $U$-utility…
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…
In this paper, we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an…
We study optimal monopoly pricing over consumer networks governed by general nonlinear utilities. In our framework, a consumer's utility is jointly determined by an individualized price and the consumption choices of their peers, propagated…
In electricity markets, customers are increasingly constrained by their budgets. A budget constraint for a user is an upper bound on the price multiplied by the quantity. However, since prices are determined by the market equilibrium, the…
We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate)…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…