naa a22 4500 51080845X CHVBK 20180411083429.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11579-013-0104-y doi (NATIONALLICENCE)springer-10.1007/s11579-013-0104-y Indifference pricing for CRRA utilities [Elektronische Daten] [Semyon Malamud, Eugene Trubowitz, Mario Wüthrich] We study utility indifference pricing of claim streams with intertemporal consumption and constant relative risk aversion utilities. We derive explicit formulas for the derivatives of the utility indifference price with respect to claims and wealth. The elegant structure of these formulas is a reflection of surprising algebraic identities for the derivatives of the optimal consumption stream. Namely, the partial derivative of the optimal consumption stream with respect to the endowment is always a projection. Furthermore, it is an orthogonal projection with respect to a natural "economic inner product”. These algebraic identities generate cancellations between the terms entering derivatives of the indifference price and allow us to prove sharp global bounds for the indifference price that become exact when the claims to wealth ratio is large and risk aversion is between one and two. For general risk aversion, we show that, in the large claims to wealth ratio limit, the asymptotic expansion of the indifference price is given in terms of fractional powers of the wealth, depending on risk aversion. When risk aversion is equal to one, the fractional power depends on the underlying claim. Springer-Verlag Berlin Heidelberg, 2013 Indifference pricing nationallicence Incomplete markets nationallicence Large risks nationallicence Malamud Semyon Swiss Finance Institute at EPFL, Quartier UNIL Dorigny, Extranef, 1015, Lausanne, Switzerland aut Trubowitz Eugene Department of Mathematics, ETH Zürich, Zurich, Switzerland aut Wüthrich Mario Department of Mathematics, ETH Zürich, Zurich, Switzerland aut Mathematics and Financial Economics Springer-Verlag 7/3(2013-06-01), 247-280 1862-9679 7:3<247 2013 7 11579 https://doi.org/10.1007/s11579-013-0104-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11579-013-0104-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Malamud Semyon Swiss Finance Institute at EPFL, Quartier UNIL Dorigny, Extranef, 1015, Lausanne, Switzerland aut NATIONALLICENCE 700 1- Trubowitz Eugene Department of Mathematics, ETH Zürich, Zurich, Switzerland aut NATIONALLICENCE 700 1- Wüthrich Mario Department of Mathematics, ETH Zürich, Zurich, Switzerland aut NATIONALLICENCE 773 0- Mathematics and Financial Economics Springer-Verlag 7/3(2013-06-01), 247-280 1862-9679 7:3<247 2013 7 11579 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer