Indifference Pricing Under Sahara Utility
Journal of Computational and Applied Mathematics
26 Pages Posted: 25 Jan 2021
Date Written: November 13, 2020
We study utility indifference pricing of untradeable 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&Forsyth2016] is consequently adopted to numerically solve the HJB equation. We determine utility indifference prices for options written on the untradeable underlying assets and some insurance contracts.
Keywords: SAHARA Utility, Indifference Pricing, Utility Maximization, Finite Difference Scheme, Incomplete Markets
JEL Classification: G11, G22, D52, C6
Suggested Citation: Suggested Citation