Quantile Optimization Under Derivative Constraint

15 Pages Posted: 7 Mar 2018

See all articles by Zuo Quan Xu

Zuo Quan Xu

Hong Kong Polytechnic University

Date Written: March 7, 2018

Abstract

This paper studies a new type of quantile optimization problems arising from insurance contract design models. This type of optimization problems is characterized by a constraint of infinity-dimension, that is, the derivatives of the decision quantile functions are bounded. Such a constraint essentially comes from the "incentive compatibility" constraint for any optimal insurance contract to avoid the potential severe problem of moral hazard in insurance contract design models. By a further development of the author's relaxation method, this paper provides a systemic approach to solving this new type of quantile optimization problems. The optimal quantile is expressed via the solution of a free boundary problem for a second-order nonlinear ordinary differential equation (ODE), which is similar to the Black-Scholes ODE for perpetual American options and has been well studied in literature theoretically and numerically.

Keywords: Quantile Optimization, Probability Weighting/Distortion, Relaxation Method, Insurance Contract Design, Free Boundary Problem, Calculus of Variations

Suggested Citation

Xu, Zuo Quan, Quantile Optimization Under Derivative Constraint (March 7, 2018). Available at SSRN: https://ssrn.com/abstract=3135689 or http://dx.doi.org/10.2139/ssrn.3135689

Zuo Quan Xu (Contact Author)

Hong Kong Polytechnic University ( email )

Hung Hom
Kowloon, 0
Hong Kong

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