Related papers: Duality Theory for Robust Utility Maximisation
This paper provides a dual formulation of the optimal consumption problem with internal multiplicative habit formation. In this problem, the agent derives utility from the ratio of consumption to the internal habit component. Due to this…
We propose a duality theory for multi-marginal repulsive cost that appear in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing…
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is…
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…
We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local)…
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…
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…
Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…
We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual…
In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…
We consider the scenario where $N$ utilities strategically bid for electricity in the day-ahead market and balance the mismatch between the committed supply and actual demand in the real-time market, with uncertainty in demand and local…
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…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function $g$ of the terminal wealth. The manager's own utility…
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.…
Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static…
We revisit the problem of maximizing expected logarithmic utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in the seminal paper of Davis and Norman [Math. Operation…
We study the sensitivity of the expected utility maximization problem in a continuous semi-martingale market with respect to small changes in the market price of risk. Assuming that the preferences of a rational economic agent are modeled…
A market model with $d$ assets in discrete time is considered where trades are subject to proportional transaction costs given via bid-ask spreads, while the existence of a num\`eraire is not assumed. It is shown that robust no arbitrage…
We consider the martingale optimal transport duality for c\`adl\`ag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of…