Hedging under an expected loss constraint with small transaction costs

2013/09/19 by Bouchard, Bruno, Moreau, Ludovic, Soner, Mete H.
#FOS: Economics and business #FOS: Mathematics #Portfolio Management (q-fin.PM) #Probability (math.PR)

paper · doi:10.48550/arxiv.1309.4916

Abstract

We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transactions is used to obtain a tractable model. A general expansion theory is developed using the dynamic programming approach. Explicit formulae are also obtained in the special cases of an exponential or power loss function. As a corollary, we retrieve the asymptotics for the exponential utility indifference price.

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