Optimal Investment and Premium Policies Under Risk Shifting and Solvency Regulation

• Date: 01 June 2015
• Author: Damir Filipović,Alexander Muermann,Robert Kremslehner
• DOI: http://doi.org/10.1111/jori.12021
• Published date: 01 June 2015

©2014 The Journal of Risk and Insurance. Vol.82, No. 2, 261–288 (2015).

DOI: 10.1111/jori.12021

Optimal Investment and Premium Policies Under

Risk Shifting and Solvency Regulation

Damir Filipovi´

c

Robert Kremslehner

Alexander Muermann

Abstract

Limited liability creates an incentive for insurers to increase the risk of the

assets and liabilities at the expense of policyholders. We show that solvency

capital requirements restrictthe set of feasible investment and premium poli-

cies and can thereby improve efficiencyunder the risk-shifting problem. This

finding becomes particularly important in light of Solvency II, the forthcom-

ing European risk-based solvency regime for insurers. We provide evidence

for Solvency II–related efficiency effects in a calibration study for a nonlife

insurer average portfolio.

Introduction

Risk shifting is a well-known agency problem in corporate finance between share-

holders and debtholders of a corporation (Jensen and Meckling, 1976; Green, 1984;

MacMinn, 1993). This agency problem is also relevant to insurance. Policyholders pay

premiums and thereby provide capital that the insurerinvests in financial assets. Lim-

ited liability provides incentives for the insurer to increase the risk of its assets and

liabilities. Other examples of such risk shifting include aggressively selling additional

policies while lowering underwriting standards or without injecting sufficient equity,

or changing the reinsurance arrangements accordingly. Risk shifting raises the insol-

Damir Filipovi´

cisatthe ´

Ecole Polytechnique F´

ed´

erale de Lausanne and Swiss Finance

Institute, Quartier UNIL-Dorigny, Extranef 218, CH-1015 Lausanne, Switzerland. Filipovi´

c

can be contacted via e-mail: damir.filipovic@epfl.ch. Robert Kremslehner is at the Depart-

ment of Finance, Accounting, and Statistics, Vienna University of Economics and Business,

Welthandelsplatz 1, Building D4, A-1020 Wien, Austria. Kremslehner can be contacted via

e-mail: robert.kremslehner@wu.ac.at. Alexander Muermann is at the Department of Finance,

Accounting, and Statistics, Vienna University of Economics and Business and ViennaGraduate

School of Finance, Welthandelsplatz 1, Building D4, A-1020 Wien, Austria. Muermann can be

contacted via e-mail: alexander.muermann@wu.ac.at. We thank Keith Crocker,Ole von H ¨

afen,

Julien Hugonnier, Christian Laux, Achim Wambach, participants of the 2010 World Risk and

Insurance Economics Congress (WRIEC), the conference "Enterprise Risk Management and

Corporate Governance for Insurance Firms" organized by ICFR and EDHEC Business School,

and two anonymous referees for helpful comments. Wegratefully acknowledge financial sup-

port by NCCR (National Centre of Competence in Research) FINRISK of the Swiss National

Science Foundation. 261

262 The Journal of Risk and Insurance

vency probability of the insurer and consequently reduces the value policyholders

attach to the insurance contract and the premium they are willing to pay for it. If the

level of investment risk cannot be specified in the insurance contract, then inefficient

investment and premium policies arise. Policyholders thus face a situation similar to

debtholders of a corporation in that both bear the cost of downside risk due to limited

liability. This incentivizes the corporation (insurer) to increase downside risk at the

expense of debtholders (policyholders).

In this article, we show that solvency regulation limits the set of feasible investment

and premium policies and can thereby address the risk-shifting problem and increase

efficiency. This observation becomes particularly important in light of Solvency II, the

forthcoming European risk-based solvency regime for insurers. We provide evidence

for Solvency II–related efficiency effects in a calibration study for a nonlife insurer

average portfolio.

More specifically, we study the economic efficiency of solvency regulation under the

risk-shifting problem in the context of a risk-neutral insurer and a risk-averse policy-

holder. We represent the risk-shifting technology by the possibility of increasing the

fraction of total capital, that is, equity and premium payments, invested in a risky

asset. The policyholder may also benefit from this investment technology for two

reasons. First, policyholders, like insurers, benefit from a positive expected return on

investment. Second, policyholders, in contrast to insurers, benefit from the hedging

potential that the investment may provide against their insurance loss.

In our benchmark, we consider Pareto optimal investment and premium policies.

We fully characterize first best Pareto optimal policies and provide a minimal set of

assumptions for their existence and uniqueness. There is no risk-shifting problem

and thus no role for solvency regulation. If, however, the fraction of total capital

invested in the risky asset cannot be specified in the insurance contract, the insurer

has an incentive to engage in risk shifting. Wecharacterize second best Pareto optimal

policies under this incentive constraint and show that they exhibit extreme investment

policies. Regulatory capital requirements restrict the set of feasible investment and

premium policies. We show that solvency regulation can thereby improve on second

best.

We then calibrate our model to a European Economic Area nonlife insurer average

portfolio taken from the QIS3 (Quantitative Impact Study 3) Benchmarking Study of

Chief Risk Officer Forum (2007) under the Solvency II standard model (see Committee

of European Insurance and Occupational Pensions Supervisors, 2010). We find that

for a wide range of the policyholder’s degree of risk aversion solvency capital re-

quirements improve on second best. But if the policyholder’s degree of risk aversion

is too low, Solvency II capital requirements can further reduce efficiency. These re-

sults are consistent with the predictions of our model. We thus provide a rationale

for risk-based insurance regulation and show its limits in addressing the risk-shifting

problem.

Our article relates to the finance literature that discusses risk shifting in a corpo-

rate setting (Jensen and Meckling, 1976; Green, 1984; MacMinn, 1993). Green (1984)