Related papers: Dynamic robust duality in utility maximization
Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this…
We consider an optimal control problem arising in the context of economic theory of growth, on the lines of the works by Skiba (1978) and Askenazy - Le Van (1999). The economic framework of the model is intertemporal infinite horizon…
Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization…
In this paper, we study the dual problem of the expected utility maximization in incomplete markets with bounded random endowment. We start with the problem formulated in the paper of Cvitani\'{c}-Schachermayer-Wang (2001) and prove the…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
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…
We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability…
We consider the utility maximization problem under convex constraints with regard to theoretical results which allow the formulation of algorithmic solvers which make use of deep learning techniques. In particular for the case of random…
We propose a new approach to utilities that is consistent with state-dependent utilities. In our model utilities reflect the level of consumption satisfaction of flows of cash in future times as they are valued when the economic agents are…
We study optimal investment strategies that maximize expected utility from consumption and terminal wealth in a pure-jump asset price model with Markov-modulated (regime switching) jump-size distributions. We give sufficient conditions for…
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 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 reveal an interesting convex duality relationship between two problems: (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market;…
In this paper we report further progress towards a complete theory of state-independent expected utility maximization with semimartingale price processes for arbitrary utility function. Without any technical assumptions we establish a…
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose…
This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of…
We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…
We consider a deterministic continuous time model of monopolistic firm, which chooses production and pricing strategies of a single good. Firm's goal is to maximize the discounted profit over infinite time horizon. The no-backlogging…