Perfect hedging under endogenous permanent market impacts |
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Authors: | Email author" target="_blank">Masaaki?FukasawaEmail author Mitja?Stadje |
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Institution: | 1.Graduate School of Engineering Science,Osaka University,Osaka,Japan;2.Faculty of Mathematics and Economics,Ulm University,Ulm,Germany |
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Abstract: | We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function, we adopt a \(g\)-expectation. In contrast to the standard framework of financial engineering, a trader is no longer a price taker as any trade has a permanent market impact via an effect on the supplier’s inventory. The P&L of a trading strategy is written as a nonlinear stochastic integral. Under this market impact model, we introduce a completeness condition under which any derivative can be perfectly replicated by a dynamic trading strategy. In the special case of a Markovian setting, the corresponding pricing and hedging can be done by solving a semilinear PDE. |
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