Related papers: Duality for optimal consumption under no unbounded…
We formulate and solve a deterministic optimal consumption problem to maximize the discounted CRRA utility of an individual's consumption-to-habit process assuming she only invests in a riskless market and that she is unwilling to consume…
We develop a regression based primal-dual martingale approach for solving finite time horizon MDPs with general state and action space. As a result, our method allows for the construction of tight upper and lower biased approximations of…
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization…
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 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…
This paper investigates an infinite horizon, discounted, consumption-portfolio problem in a market with one bond, one liquid risky asset, and one illiquid risky asset with proportional transaction costs. We consider an agent with liquidity…
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context…
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
This paper considers an initial market model, specified by its underlying assets $S$ and its flow of information $\mathbb F$, and an arbitrary random time $\tau$ which might not be an $\mathbb F$-stopping time. As the death time and the…
We propose martingale consumption as a natural, desirable consumption pattern for any given (proportional) investment strategy. The idea is to always adjust current consumption so as to achieve level expected future consumption under the…
In this paper, we work in the framework of the Merton problem but we impose a drawdown constraint on the consumption process. This means that consumption can never fall below a fixed proportion of the running maximum of past consumption. In…
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 concerns the recursive utility maximization problem. We assume that the coefficients of the wealth equation and the recursive utility are concave. Then some interesting and important cases with nonlinear and nonsmooth…
We consider infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost.…
We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random…
The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only…
Density function describes the density of states in the state space of a dynamic system or a Markov Decision Process (MDP). Its evolution follows the Liouville equation. We show that the density function is the dual of the value function in…
For utility functions $u$ finite valued on $\mathbb{R}$, we prove a duality formula for utility maximization with random endowment in general semimartingale incomplete markets. The main novelty of the paper is that possibly non locally…
We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in a previous paper under…