Insurance Market Effects of Risk Management Metrics

Abstract

We extend the classical analysis on optimal insurance design to the case when the insurer implements regulatory requirements (Value-at-Risk). Presumably, regulators impose some risk management requirement such as VaR to reduce the insurers' insolvency risk, as well as to improve the insurance market stability. We show that VaR requirements may better protect the insured and improve economic efficiency, but have stringent negative effects on the insurance market. Our analysis reveals that the insured are better protected in the event of greater loss irrespective of the optimal design from either the insured or the insurer perspective. However, in the presence of the VaR requirement on the insurer, the insurer's insolvency risk might be increased and there are moral hazard issues in the insurance market because the optimal contract is discontinuous. IntroductionThis paper shows that Value-at-Risk (VaR) regulatory requirements have controversial effects on the insurance market. On the one hand, the insured are better protected in the event of a large loss irrespective of the optimal design from either the insured's or the issuer's side, when the insurer implements VaR imposed by regulators. On the other hand, since the insurer then covers more, when a large loss occurs, the default risk of the insurer is increased, as well as the instability of the market. Moreover, because of the presence of discontinuities in the optimal insurance contract presented in this paper, the optimal risk sharing introduces moral hazard issues in the insurance market.The Geneva Risk and Insurance Review, 2010, 35, (47-80) r 2010 The International Association for the Study of Insurance Economics 1554-964X/10 www.palgrave-journals.com/grir/ VaR is not a new concept in risk management. Recommendations on banking laws and regulations issued by the Basel Committee on Banking Supervision have been implemented in the banking sector. In Basel I and Basel II, the VaR methodology is used to deal with the market risk and the credit risk. Similarly, in Solvency II 1 for the insurance sector, the economic capital could be calculated by an internal VaR model. However, whether VaR risk management 2 requirements really enhance the efficiency and stability of the market still remains elusive. For instance, in the context of financial market, Basak and Shapiro (2001) derive that the presence of VaR risk managers amplifies the stock-market volatility in a downward market and attenuates the volatility in an upward market. The 2007-2008 global financial crises lead to even more serious concerns on the adequacy of VaR methodology to deal with credit risk. This paper reveals some negative aspects of the regulatory VaR methodology in the insurance market.We develop a theoretical framework to investigate the economic consequences for the insured and to the insurance market in the presence of regulatory risk management requirements on insurers. This study is done under the expected utility paradigm and the risk management requirement is interpreted as a VaR c...

Optimal risk sharing under distorted probabilities

“…Such H h is not consistent with the ≤ cx -order, and therefore Lemma 2 does not apply. Indeed, as explicitly shown by Bernard and Tian [6], the resulting optimal allocation might fail to be comonotone.…”

“…This of course modifies the resulting Pareto optimal allocations since some of the possible optima become infeasible under the constraint. A similar model was studied by Bernard and Tian [6] under the assumption of a VaR constraint. In our framework where we work with distortion risk measures, we instead postulate constraints of the form…”

“…Instead of considering all these cases for an arbitrary n, in Sects. 5.3 and 6 we focus on a simple example with two agents and one constraint, a setting already taken up in Bernard and Tian [6].…”

“…The latter problem, which we call risk sharing under constraints, introduces effectively n + 1 players into the model, namely n original participants, plus the additional regulator that imposes limits on allowable risk exposures of each participant. The special case of Value-at-Risk constraints was recently analyzed in Bernard and Tian [6].…”

Risk Measures and Capital Requirements: A Critique of the Solvency II Approach

“…7 Cf., among others, Cuoco and Liu (2006); Leippold et al (2006). 8 Bernard and Tian (2010). Alberto Floreani Risk Measures and Capital Requirements insurance contracts at time t¼0 which gives a random cash outflow for claims and expenses equal to L˜1 at time t¼1.…”