Realization Utility with Path-Dependent Reference Points

Forthcoming, SIAM Journal on Financial Mathematics

50 Pages Posted: 12 Apr 2021 Last revised: 8 Jun 2022

See all articles by Linghui Kong

Linghui Kong

Soochow University

Cong Qin

Soochow University

Xingye Yue

affiliation not provided to SSRN

Date Written: April 10, 2021

Abstract

In this paper, we propose a model to study the impact of path-dependent reference points on optimal trading strategies of a realization utility investor, where the reference points are initial purchase prices adjusted dynamically by subsequent paper gains and losses. By homogeneity, this optimal trading problem can be reformulated as a new one with a unique state variable x (wealth-reference ratio), which can be solved analytically. Importantly, we find that the introduction of path-dependent reference points can generate two interesting effects: (a) Discount effect, i.e., a constant subjective discount factor in the original problem becomes stochastic in the new problem; and (b) Mean-reverting effect, i.e., the state variable x follows a mean-reverting process. These two effects offset each other in the state of paper gain (x > 1) while getting reinforced in the state of paper loss (x < 1), leading to a disposition effect even if a subjective discount factor in the original problem is zero. Finally, the model can be easily extended to incorporate other factors such as asymmetric adaptation of reference points, jump risks in the underlying stocks, and liquidation shocks.

Keywords: Realization Utility, Path-Dependent Reference Points, Variational Inequality, Penalty Method

JEL Classification: G02, C61

Suggested Citation

Kong, Linghui and Qin, Cong and Yue, Xingye, Realization Utility with Path-Dependent Reference Points (April 10, 2021). Forthcoming, SIAM Journal on Financial Mathematics, Available at SSRN: https://ssrn.com/abstract=3823813 or http://dx.doi.org/10.2139/ssrn.3823813

Linghui Kong

Soochow University ( email )

No. 1 Shizi Street
Taipei, Jiangsu 215006
Taiwan

Cong Qin (Contact Author)

Soochow University ( email )

No. 1 Shizi Street, Center for Financial Engineeri
Suzhou, 215006
China
13656190706 (Phone)

Xingye Yue

affiliation not provided to SSRN ( email )

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