Optimal reinsurance and portfolio selection: Comparison between partial and complete information models

• Published date: 01 January 2022
• Author: Bong‐Gyu Jang,Kyeong Tae Kim,Hyun‐Tak Lee
• Date: 01 January 2022
• DOI: http://doi.org/10.1111/eufm.12303

DOI: 10.1111/eufm.12303

ORIGINAL ARTICLE

Optimal reinsurance and portfolio selection:

Comparison between partial and complete

information models

Bong‐Gyu Jang

1

|Kyeong Tae Kim

2

|Hyun‐Tak Lee

3

1

Department of Industrial and

Management Engineering, POSTECH,

Pohang, Republic of Korea

2

Big Data & AI Lab, Hana Institute of

Technology, Hana TI, Seoul,

Republic of Korea

3

KAMCO Research Center, Korea Asset

Management Corporation, Busan,

Republic of Korea

Correspondence

Hyun‐Tak Lee, Korea Asset Management

Corporation, BIFC, 40,

Munhyeongeumyung‐Ro, Nam‐Gu,

Busan 48400, Republic of Korea.

Email: lht1107@gmail.com

Abstract

We consider partial and complete information models

to investigate how partial information has a unique

quality over complete information for insurers. We find

that optimal reinsurance and investment strategies for

the partially informed insurer depend on prior beliefs,

whereas those for the completely informed insurer do

not. In addition, information quality can affect insurer

behaviour, mainly through the relative difference be-

tween risk‐adjusted market premium and risk‐adjusted

insurance premium projected on the financial markets.

Numerical results indicate that partial information

increases the conservativeness of insurer strategies.

KEYWORDS

certainty equivalent wealth, information quality, partial

information, risk‐adjusted premium

JEL CLASSIFICATION

C61; G11; G22

EUROPEAN

FINANCIAL MANAGEMENT

Eur Financ Manag. 2022;28:208–232.wileyonlinelibrary.com/journal/eufm208

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© 2021 John Wiley & Sons Ltd.

We would like to thank John A. Doukas (the editor) and an anonymous referee for their valuable and constructive

comments. Also, we are grateful to Byeong‐Je An, Chang Hui Choi, Hyung‐Suk Choi, Jiwook Jang, Hyeng Keun Koo,

Bong Soo Lee, Jaeram Lee, Seyoung Park, Yong Hyun Shin and all participants at the 2017 Co‐conference in Finance of

Korea, the 13th Annual Conference of the Asia‐Pacific Association of Derivatives (APAD) and the 2015 International

Conference on Control Theory and Mathematical Finance for helpful suggestions. All errors and omissions are our

own. This paper is a revised version of Chapter 3 of Kyeong Tae Kim's Ph.D. dissertation submitted to the Department

of Industrial and Management Engineering, POSTECH. National Research Foundation of Korea, Grant/Award

Number: NRF‐2020R1A2B5B01001721.

1|INTRODUCTION

Asset prices and transactions react to new information. In modern financial markets, investors

have access to a large amount of information, including macroeconomic, corporate and poli-

tical news. It is important to have information with different levels of quality because such

information can change investor expectations, which are subsequently reflected in asset prices

and market participant transaction behaviour. For this reason, a growing body of literature

explores the implications of information quality for parameter learning on asset prices (Adam

et al., 2016; Ai, 2010; Collin‐Dufresne et al., 2016; Epstein & Schneider, 2008; Veronesi, 2000)

and investment decisions (Honda, 2003; Lee, 2016; Liu, 2011; Wang, 2009).

Conventional studies commonly assume that investors do not have complete knowledge of

probability distributions of market variables, that is, investors have only partial information

(PI). Several studies explore investor behaviour in the absence of complete information (CI) in

the financial markets. Song and Yang (2014) investigate pricing, timing and hedging methods

for American call options in a partially informed situation. Ceci et al. (2014) derive risk‐

minimizing hedging strategies when information available to investors is restricted and they

are provided optimal hedging strategies for unit‐linked life insurance contracts. Y. Li et al.

(2015) implement a mean‐variance portfolio selection when the risky asset price process is not

directly observable in the financial market. Indeed, investors that have such PI tend to make

forward‐looking decisions that differ from those of investors with CI (Hansen, 2007). To the best

of our knowledge, little research considers how PI has unique information quality over CI. Our

motivation comes from Ang and Bekaert (2002), who state:

Under the alternative assumption where investors are uncertain about the regimes, the effects

of regime‐switching would be weaker since the regime‐dependent solutions would

deviate less from the i.i.d. solution. (p. 1142)

Among major participants in financial markets, insurers are representative long‐term in-

vestors who invest in massive assets and are required to invest very safely. However, over their

long investment horizon, economic conditions can change considerably such that insurers are

more likely to be exposed to risk from PI than are short‐term investors.

Many studies consider insurer optimal reinsurance and asset allocation problems.

Promislow and Young (2005) derive an analytic solution to the ruin‐minimization problem of

an insurer under the assumption that the insurance claims process follows a drifted Brownian

motion. Using a similar setting, Cao and Wan (2009) provide an analytic solution to maximize

the insurer's utility of terminal wealth. Guan and Liang (2014) consider the problem that

insurers are exposed to risk from interest and inflation; to make the market complete, they use

a zero‐coupon bond and Treasury Inflation‐Protected Securities (TIPS) in addition to a bank

account and a risky stock. Jang and Kim (2015) extend the insurer's ruin‐minimization model

to consider a regime‐switching market environment and show that optimal strategies could be

nonmyopic. Zhu et al. (2015) consider an insurer's problem under counterparty risk; they adopt

a defaultable asset such as a corporate bond and solve it by decomposing the original problem

into a pre‐default problem and a post‐default problem. Recently, some studies consider an

ambiguity‐averse insurer and solve the insurer's problem in various settings (Gu et al., 2017;

D. Li et al., 2018; D. Li & Young, 2019; Zheng et al., 2016). For instance, Chen and Yang (2020)

solve the insurer's problem when an ambiguity‐averse insurer's future claims are correlated

with historical claims. However, most existing literature concerning optimal reinsurance as-

sumes CI, and little research considers PI.

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