Risk measure optimization: Perceived risk and overconfidence of structured product investors

Xi Chen; Zongrun Wang; Songhai Deng; Yong Fang

doi:10.3934/jimo.2018105

Article Contents

2019, Volume 15, Issue 3: 1473-1492. Doi: 10.3934/jimo.2018105

This issue Previous Article Online and offline cooperation under buy-online, pick-up-in-store: Pricing and inventory decisions Next Article Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs

Risk measure optimization: Perceived risk and overconfidence of structured product investors

1.
School of Business, Central South University, Changsha, China
2.
School of Mathematics and Statistics, Central South University, Changsha, China
3.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

* Corresponding author: Zongrun Wang
* Corresponding author: Zongrun Wang

Received: December 31, 2017

Revised: February 28, 2018

Early access: June 2018

Published: April 2019

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Abstract

In financial optimization, it is important to quantify the risk of structured financial products. This paper quantifies the risk of structured financial products by perceived risk measures based on a standard measure of risk, and then we construct the risk perception and decision-making models of individual investors considering structured products. Moreover, based on bullish and bearish binary structured products, we introduce the psychological bias of overconfidence to explore how this bias affects investors' perceived risk. This study finds that overconfident investors believe in private signals and underestimate the variance of noise in private signals, which affects their expectation of the underlying asset price of structured financial products. Furthermore, overconfidence bias leads investors to overestimate the probability of obtaining a better return. With the increase in overconfidence, the overestimation of the probability is intensified, which eventually leads to lower perceived risk.

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Mathematics Subject Classification: Primary: 91B08, 91E10; Secondary: 91G20.

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Figure 1. The lottery form of binary structured financial products

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Figure 2. Expected price distribution of overconfident investors when $\theta+\varepsilon>\mu$

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Figure 3. Expected price distribution of overconfident bullish investors of type Ⅰ

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Figure 4. Expected price distribution of overconfident bullish investors of type Ⅱ

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Figure 5. Expected price distribution of overconfident bullish investors of type Ⅲ

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Figure 6. Perceived risk of overconfident bullish investors of type Ⅰ

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Figure 7. Perceived risk of overconfident bullish investors of type Ⅱ or type Ⅲ(2)(4)

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Figure 8. Perceived risk of overconfident bullish investors of type Ⅲ(3)

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