Related papers: Duality for optimal consumption under no unbounded…
Consider a financial market with nonnegative semimartingales which does not need to have a num\'{e}raire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities,…
We study a doubly tactic resource consumption model \bess \left\{\begin{array}{lll} u_t=\tr u-\nabla\cd(u\nabla w),\\[1mm] v_t=\tr v-\nabla\cd(v\nabla u)+v(1-v^{\beta-1}),\\[1mm] w_t=\tr w-(u+v)w-w+r \end{array}\right. \eess in a smooth…
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…
We continue the analysis of our previous paper (Czichowsky/Schachermayer/Yang 2014) pertaining to the existence of a shadow price process for portfolio optimisation under proportional transaction costs. There, we established a positive…
We identify the effective theory describing inflationary super-Hubble scales and show it to be a special case of effective field theories appropriate to open systems. Open systems allow information to be exchanged between the degrees of…
We investigate optimal consumption policies in the liquidity risk model introduced in Pham and Tankov (2007). Our main result is to derive smoothness results for the value functions of the portfolio/consumption choice problem. As an…
In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market…
We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can…
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…
This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems…
We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing -- a menu of product bundles that are nested in the strong set order. Our approach…
Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is…
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…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…
The consumption function maps current wealth and the exogenous state to current consumption. We prove the existence and uniqueness of a consumption function when the agent has a preference for wealth. When the period utility functions are…
We consider an optimal investment-consumption problem for a utility-maximizing investor who has access to assets with different liquidity and whose consumption rate as well as terminal wealth are subject to lower-bound constraints. Assuming…
We study the sequential decision making problem of maximizing the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon…
This article develops a numerical approximation of a convex non-local and non-smooth minimization problem. The physical problem involves determining the optimal distribution, given by $h\colon \Gamma_I\to [0,+\infty)$, of a given amount…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…