Indifference Pricing under SAHARA UtilityApplications in Insurance and Finance (Joint work with An Chen and Thai Ngyuen)
Pricing claims on nontraded assets is one of the ongoing challenges in option pricing theory. Nontraded assets occur in many different settings this can e.g. be illiquid stocks, real estate or death probabilities in insurance contracts. A usual way to hedge claims on a nontraded asset is to trade in correlated assets to reduce the risk of unfavorable market development. One way to price such claims is by using utility indifference pricing. Since Power and Exponential utility functions are restricted to positive payouts we aim to derive new results for the more general SAHARA utility function. We will compare our results with known results for Power and Exponential utility as well as we want to extend the known results to more complex products and seller prices. Since we do not have any analytic solutions in the incomplete market setting we rely on a dynamic programming approach and set up a HJB equation, which we will solve with a numerical algorithm.