Indifference Pricing Under Sahara Utility

Abstract

Abstract We study utility indifference pricing of untradable assets in incomplete markets using a symmetric asymptotic hyperbolic absolute risk aversion (SAHARA) utility function, both from the buyer’s and seller’s perspective. The use of the SAHARA utility function allows us to tackle the “short call” problem, which power and exponential utility functions are unable to solve. While no closed-form solutions are available for the indifference prices, we are able to derive some pricing bounds. Furthermore, we rely on the dynamic programming approach to solve the associated utility maximization problem, which leads to a two-dimension HJB equation. A complex algorithm discussed in Ma and Forsyth (2016) is consequently adopted to numerically solve the HJB equation. We determine utility indifference prices for options written on the untradable underlying assets and some insurance contracts.