Optimal Insurance to Maximize Exponential Utility When Premium is Computed by a Convex Functional

Forthcoming in SIAM Journal on Financial Mathematics

12 Pages Posted: 13 Feb 2024

See all articles by Jingyi Cao

Jingyi Cao

York University

Dongchen Li

York University

V.R. Young

University of Michigan at Ann Arbor - Department of Mathematics

Bin Zou

University of Connecticut - Department of Mathematics

Date Written: January 15, 2024

Abstract

We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the candidate optimal indemnity is given implicitly, we use that necessary condition to develop a numerical algorithm to compute it. We prove that the numerical algorithm converges to a unique indemnity that, indeed, equals the optimal policy. We also illustrate our results with numerical examples.

Keywords: Optimal insurance, numerical algorithm, convex premium functional

Suggested Citation

Cao, Jingyi and Li, Dongchen and Young, Virginia R. and Zou, Bin, Optimal Insurance to Maximize Exponential Utility When Premium is Computed by a Convex Functional (January 15, 2024). Forthcoming in SIAM Journal on Financial Mathematics, Available at SSRN: https://ssrn.com/abstract=4695235

Jingyi Cao

York University ( email )

4700 Keele Street
Toronto, M3J 1P3
Canada

Dongchen Li

York University ( email )

4700 Keele Street
Toronto, M3J 1P3
Canada

Virginia R. Young

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States
734-764-7227 (Phone)

Bin Zou (Contact Author)

University of Connecticut - Department of Mathematics ( email )

341 Mansfield Road U1009
Department of Mathematics
Storrs, CT 06269-1069
United States

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