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An asymptotic approach to centrally planned portfolio selection

Part of: Mathematical economics Mathematical finance

Published online by Cambridge University Press:  08 February 2024

Zongxia Liang  and
Yang Liu Open the ORCID record for Yang Liu [Opens in a new window]
Zongxia Liang*
Affiliation:
Tsinghua University
Yang Liu*
Affiliation:
The Chinese University of Hong Kong, Shenzhen
*
*Postal address: Department of Mathematical Sciences, Tsinghua University, 30 Shuangqing Road, Haidian Dist, Beijing 100084, China. Email address: [email protected]
**Postal address: Division of Mathematics, School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, 2001 Longxiang Blvd, Longgang Dist, Shenzhen, Guangdong 518172, China. Email address: [email protected]
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Abstract

We formulate a centrally planned portfolio selection problem with the investor and the manager having S-shaped utilities under a recently popular first-loss contract. We solve for the closed-form optimal portfolio, which shows that a first-loss contract can sometimes behave like an option contract. We propose an asymptotic approach to investigate the portfolio. This approach can be adopted to illustrate economic insights, including the fact that the portfolio under a convex contract becomes more conservative when the market state is better. Furthermore, we discover a means of Pareto improvement by simultaneously considering the investor’s utility and increasing the manager’s incentive rate. This is achieved by establishing the collection of Pareto points of a single contract, proving that it is a strictly decreasing and strictly concave frontier, and comparing the Pareto frontiers of different contracts. These results may be helpful for the illustration of risk choices and the design of Pareto-optimal contracts.

Keywords

Utility theoryfirst-loss contractasymptotic analysisPareto improvement

MSC classification

Primary: 91B16: Utility theory
Secondary: 91G10: Portfolio theory
Type
Original Article
Information
Advances in Applied Probability , Volume 56 , Issue 3 , September 2024 , pp. 757 - 784
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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