Related papers: Infinite horizon utility maximisation from inter-t…
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the…
We propose \textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a…
We consider an arbitrage-free, discrete time and frictionless market. We prove that an investor maximising the expected utility of her terminal wealth can always find an optimal investment strategy provided that her dissatisfaction of…
We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger…
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 study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR…
We establish strong duality relations for functional two-step compositional risk-constrained learning problems with multiple nonconvex loss functions and/or learning constraints, regardless of nonconvexity and under a minimal set of…
A finite-horizon optimal estimation problem for discrete-time linear systems is formulated and solved. The formulation is a natural extension of that which yields a deadbeat observer. The resultant observer is the dual of the controller…
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…
In the context of large financial markets we formulate the notion of \emph{no asymptotic free lunch with vanishing risk} (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an…
We establish when the two problems of minimizing a function of lifetime minimum wealth and of maximizing utility of lifetime consumption result in the same optimal investment strategy on a given open interval $O$ in wealth space. To answer…
We consider the problem of tabular infinite horizon concave utility reinforcement learning (CURL) with convex constraints. For this, we propose a model-based learning algorithm that also achieves zero constraint violations. Assuming that…
In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker…
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…
In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a…
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 study the portfolio selection problem of a long-run investor who is maximising the asymptotic growth rate of her expected utility. We show that, somewhat surprisingly, it is essentially not affected by introduction of a floor constraint…
This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi-asset…
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…
The aim of this short note is to present a solution to the discrete time exponential utility maximization problem in a case where the underlying asset has a multivariate normal distribution. In addition to the usual setting considered in…