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.

从买方和卖方的角度，我们使用对称渐近双曲线绝对风险规避（SAHARA）效用函数研究不完全市场中不可交易资产的效用无差异定价。使用SAHARA实用程序功能使我们能够解决“幂函数”和指数实用程序无法解决的“短呼叫”问题。尽管没有针对无差别价格的封闭式解决方案，但我们能够得出一些定价范围。此外，我们依靠动态规划方法来解决相关的效用最大化问题，这导致了二维HJB方程。因此，采用了Ma和Forsyth（2016）中讨论的复杂算法来对HJB方程进行数值求解。