Convex duality in optimal investment under illiquidity

@article{Pennanen2014ConvexDI,
  title={Convex duality in optimal investment under illiquidity},
  author={T. Pennanen},
  journal={Mathematical Programming},
  year={2014},
  volume={148},
  pages={279-295}
}
  • T. Pennanen
  • Published 2014
  • Mathematics, Computer Science
  • Mathematical Programming
We study the problem of optimal investment by embedding it in the general conjugate duality framework of convex analysis. This allows for various extensions to classical models of liquid markets. In particular, we obtain a dual representation for the optimum value function in the presence of portfolio constraints and nonlinear trading costs that are encountered e.g. in modern limit order markets. The optimization problem is parameterized by a sequence of financial claims. Such a… Expand
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References

SHOWING 1-10 OF 53 REFERENCES
Convex Duality in Constrained Portfolio Optimization
We study the stochastic control problem of maximizing expected utility from terminal wealth and/or consumption, when the portfolio is constrained to take values in a given closed, convex subset ofExpand
Dual representation of superhedging costs in illiquid markets
This paper studies superhedging of contingent claims in illiquid markets where trading costs may depend nonlinearly on the traded amounts and portfolios may be subject to constraints. We give dualExpand
Arbitrage and deflators in illiquid markets
  • T. Pennanen
  • Economics, Computer Science
  • Finance Stochastics
  • 2011
TLDR
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by conveX sets and their relations to state price deflators are studied. Expand
Optimal investment and contingent claim valuation in illiquid markets
  • T. Pennanen
  • Economics, Computer Science
  • Finance Stochastics
  • 2014
TLDR
The existence of optimal trading strategies and the lower semicontinuity of the optimal value of optimal investment under conditions that extend the no-arbitrage condition in the classical linear market model are established. Expand
Superhedging in Illiquid Markets
We study superhedging of securities that give random payments possibly at multiple dates. Such securities are common in practice where, due to illiquidity, wealth cannot be transferred quite freelyExpand
Transaction Costs and Shadow Prices in Discrete Time
For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the sameExpand
Transaction Costs, Shadow Prices, and Connections to Duality
For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the sameExpand
Optimal investment with transaction costs and without semimartingales
We consider a general class of optimization problems in financial markets with incomplete information and transaction costs. Under a noarbitrage condition strictly weaker than the existence of aExpand
Optimal Consumption from Investment and Random Endowment in Incomplete Semimartingale Markets
We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence andExpand
Modeling Liquidity Effects in Discrete Time
We study optimal portfolio choices for an agent with the aim of maximising utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence ofExpand
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