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Asymptotic lower bounds for optimal tracking: A linear programming approach

Jiatu Cai · Mathieu Rosenbaum · Peter Tankov

25 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Stability and Control of Uncertain Systems Risk and Portfolio Optimization

Abstract

We consider the problem of tracking a target whose dynamics is modeled by a continuous Itô semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. A comprehensive list of examples with explicit expressions for the lower bounds is provided.

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References

1999Continuous Martingales and Brownian Motion 1997An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs 2001Heavy Traffic Analysis of Controlled Queueing and Communication Networks 1998Existence of Markov Controls and Characterization of Optimal Markov Controls 1999Some applications of impulse control in mathematical finance 2010THE COST OF ILLIQUIDITY AND ITS EFFECTS ON HEDGING 2000Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves 1998Optimal stochastic intervention control with application to the exchange rate

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