General indifference pricing with small transaction costs

Article type: Research Article

Authors: Possamaï, Dylan^{a; *} | Royer, Guillaume^b

Affiliations: [a] CEREMADE, Université Paris Dauphine, France | [b] CMAP, Ecole Polytechnique Paris, France

Correspondence: [*] Corresponding author: Dylan Possamaï, CEREMADE, Université Paris Dauphine. Tel.: +33 (0)1 44-05-47-32; Fax: +33 (0)1 44-05-45-99; E-mail: possamai@ceremade.dauphine.fr.

Abstract: 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 [SIAM Journal on Control and Optimization 51 (2013), 2893–2921] and [Communications in Partial Differential Equations 40 (2015), 2005–2046] 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 [SIAM Journal on Financial Mathematics 3 (2012), 433–458].

Keywords: Transaction costs, homogenization, viscosity solutions, utility indifference pricing, asymptotic expansions

DOI: 10.3233/ASY-171415

Journal: Asymptotic Analysis, vol. 102, no. 3-4, pp. 177-226, 2017