The Feedback Effect of Hedging in Portfolio Optimization.pdfVIP

Preprint submitted to International Journal of Theoretical and Applied Finance c World Scientific Publishing Company 4 0 0 2 The Feedback Effect of Hedging in Portfolio Optimization r p A ` P. HENRY-LABORDERE 1 Theoretical Physics Group, The Blackett Laboratory, Imperial College London 2 Prince Consort Road, London SW7 2AZ, U.K. phenry@lpt.ens.fr ] r e h t In this short note, we will show how to optimize the portfolio of a large trader whose o hedging strategy affects the price of his assets. . t a Keywords : Illiquid Market, feedback effect, stochastic optimization m - d 1. Introduction n 1 o Since the famous papers of Black-Scholes on option pricing and of Markowitz on c portfolio optimization 2 (for a review 3 ), some progress has been made in order to [ extend these results to a more realistic arbitrage-free market model. As a reminder, 1 the Black-Scholes theory and the Markowitz’s theory consist in following a (hedging) v strategy to decrease the risk of loss given a fixed amount of return. Both theories 0 2 are based on three important hypothesis which are satisfied only to a certain extent: 5 4 • The traders can revise their decisions continuously