Related papers: Duality Theory for Robust Utility Maximisation
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics.…
We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…
Duality is a foundational tool in robust and distributionally robust optimization (RO and DRO), underpinning both analytical insights and tractable reformulations. The prevailing approaches in the literature primarily rely on saddle-point…
In this letter, we model the day-ahead price-based demand response of a residential household with battery energy storage and other controllable loads, as a convex optimization problem. Further using duality theory and Karush-Kuhn-Tucker…
We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the…
Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff. Economic intuition suggests that…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…
With the tremendous increase of the Internet traffic, achieving the best performance with limited resources is becoming an extremely urgent problem. In order to address this concern, in this paper, we build an optimization problem which…
We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely…
Using duality theory techniques we derive simple, closed-form formulas for bounding the optimal revenue of a monopolist selling many heterogeneous goods, in the case where the buyer's valuations for the items come i.i.d. from a uniform…
We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our…
We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case,…
We investigate optimal consumption problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall for logarithmic utility functions. We find the solutions in terms of a dynamic strategy in explicit…
This paper presents a class of passivity-based cooperative control problems that have an explicit connection to convex network optimization problems. The new notion of maximal equilibrium independent passivity is introduced and it is shown…
The recent research report of U.S. Department of Energy prompts us to re-examine the pricing theories applied in electricity market design. The theory of spot pricing is the basis of electricity market design in many countries, but it has…
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 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 investigate optimal consumption and investment problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall. We formulate various utility maximization problems, which can be solved explicitly. We…