Indifference Pricing Under Sahara Utility

Journal of Computational and Applied Mathematics

26 Pages Posted: 25 Jan 2021

See all articles by An Chen

An Chen

University of Ulm

Thai Nguyen

University of Ulm - Institute of Insurance Science

Nils Sørensen

University of Ulm

Date Written: November 13, 2020

Abstract

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

Chen, An and Nguyen, Thai and Sørensen, Nils, Indifference Pricing Under Sahara Utility (November 13, 2020). Journal of Computational and Applied Mathematics, Available at SSRN: https://ssrn.com/abstract=3730609 or http://dx.doi.org/10.2139/ssrn.3730609

An Chen

University of Ulm ( email )

Helmholtzstrasse 20
Ulm, D-89081
Germany

HOME PAGE: http://www.uni-ulm.de/mawi/ivw/team

Thai Nguyen

University of Ulm - Institute of Insurance Science ( email )

Ulm, 89081
Germany

Nils Sørensen (Contact Author)

University of Ulm ( email )

Albert-Einstein-Alee 11
Ulm, D-89081
Germany

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