Related papers: Duality Theory for Portfolio Optimisation under Tr…
In the present work we develop a formalism to tackle the problem of optimal execution when trading market securities. More precisely, we introduce a utility function that balances market impact and timing risk, with this last being modelled…
This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic…
We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to $k$ trades, where each trade must involve the…
We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…
This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows that by using the canonical duality…
We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non…
We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the…
In this paper, we study expected utility maximization under ratchet and drawdown constraints on consumption in a general incomplete semimartingale market using duality methods. The optimization is considered with respect to two parameters:…
In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…
An agent-based modelling methodology for the joint price evolution of two stocks is put forward. The method models future multidimensional price trajectories reflecting how a class of agents rebalance their portfolios in an operational way…
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from…
We study optimal liquidation in the presence of linear temporary and transient price impact along with taking into account a general price predicting finite-variation signal. We formulate this problem as minimization of a cost-risk…
This paper considers the finite horizon portfolio rebalancing problem in terms of mean-variance optimization, where decisions are made based on current information on asset returns and transaction costs. The study's novelty is that the…
We prove limit theorems for the super-replication cost of European options in a Binomial model with friction. The examples covered are markets with proportional transaction costs and the illiquid markets. The dual representation for the…
We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is…
Convergence (virtual) bidding is an important part of two-settlement electric power markets as it can effectively reduce discrepancies between the day-ahead and real-time markets. Consequently, there is extensive research into the bidding…
We propose a method for providing communication network infrastructure in autonomous multi-agent teams. In particular, we consider a set of communication agents that are placed alongside regular agents from the system in order to improve…
We study contingent claims in a discrete-time market model where trading costs are given by convex functions and portfolios are constrained by convex sets. In addition to classical frictionless markets and markets with transaction costs or…