Indifference Pricing for Power Utilities
We study utility indiﬀerence pricing of claim streams with intertem- poral consumption and power (CRRA) utilities. We derive explicit for- mulas for the derivatives of the utility indiﬀerence price with respect to claims and wealth. The simple structure of these formulas is a reﬂec- tion of surprising operator identities for the derivatives of the optimal consumption stream. For example, the partial derivative of the opti- mal consumption stream with respect to the endowment is always a pro jection. Furthermore, it is an orthogonal pro jection with respect to a natural ”economic inner product”. We ﬁnd that the indiﬀerence price is a highly non-linear function of the wealth and obtain its asymptotic behavior when the claims to wealth ratio is either very small or very large. 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. We also obtain sharp global bounds for the indiﬀerence price.
Record created on 2009-10-12, modified on 2016-08-08