General indifference pricing with small transaction costs. (English) Zbl 1366.35195
Summary: We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and a general utility function at final time \(T\) , we obtain an asymptotic expansion of the utility indifference price as a function of the asymptotic expansions of the utility maximization problems with and without the European contingent claim. We use the tools developed in [H. M. Soner and N. Touzi, SIAM J. Control Optim. 51, No. 4, 2893–2921 (2013; Zbl 1280.91158)] and [the first author et al., Commun. Partial Differ. Equations 40, No. 11, 2005–2046 (2015; Zbl 1366.91144)] based on homogenization and viscosity solutions to characterize these expansions. Finally we study more precisely the example of exponential utilities, in particular recovering under weaker assumptions the results of M. Bichuch [SIAM J. Financ. Math. 3, 433–458 (2012; Zbl 1255.91390)].
MSC:
| 35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 35D40 | Viscosity solutions to PDEs |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 91G10 | Portfolio theory |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
Keywords:
transaction costs; homogenization; viscosity solutions; utility indifference pricing; asymptotic expansionsReferences:
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