A Classification Approach to General S-Shaped Utility Optimization with Principals' Constraints

SIAM J. Control Optim., 58(6), 3734-3762.

30 Pages Posted: 11 Dec 2019 Last revised: 21 Dec 2020

See all articles by Zongxia Liang

Zongxia Liang

affiliation not provided to SSRN

Yang Liu

Tsinghua University - Department of Mathematical Sciences

Date Written: November 12, 2019

Abstract

We study a problem in the principal-agent model of two general S-shaped utilities without explicit expressions, where the two parties have different reference points. The problem is featured with a principal's participating incentive compatible constraint, which particularly stands in the context of asset management with motivation to safeguard the benefit of the principal. After a thorough investigation, it turns out to be a complicated double S-shaped utility optimization problem. We propose a new classification approach to study the optimal final asset allocation. First, it is classified into two cases: (a) One-side-loss case in which either both parties suffer liquidation, or one gains and the other loses, or both make profit. (b) Option case in which either both parties suffer liquidation or both make profit. Further, we demonstrate an asymptotic classification of the optimal asset allocation that the single utility maximization of the principal is the limit of the option case, while that of the agent is the limit of the one-side-loss case. More importantly, we find a division reservation utility which the optimal asset allocation belongs to the option case beyond and to the one-side-loss case below. Thus, the key factor resulting in different risk choices is the size of the reservation utility. As an application, we numerically visualize these results with a specific participating contract, which illustrates some novel mechanisms in asset management.

Keywords: Principal-agent problem, Double S-shaped utility optimization, Optimal asset allocation, Classfication

JEL Classification: G11, C61

Suggested Citation

Liang, Zongxia and Liu, Yang, A Classification Approach to General S-Shaped Utility Optimization with Principals' Constraints (November 12, 2019). SIAM J. Control Optim., 58(6), 3734-3762. , Available at SSRN: https://ssrn.com/abstract=3492712 or http://dx.doi.org/10.2139/ssrn.3492712

Zongxia Liang

affiliation not provided to SSRN

Yang Liu (Contact Author)

Tsinghua University - Department of Mathematical Sciences ( email )

Beijing, 100084
China

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