Optimal reinsurance with expectile

In this paper, we study optimal reinsurance treaties that minimize the liability of an insurer. The liability is defined as the actuarial reserve on an insurer’s risk exposure plus the risk margin required for the risk exposure. The risk margin is determined by the risk measure of expectile. Among a general class of reinsurance premium principles, we prove that a two-layer reinsurance treaty is optimal. Furthermore, if a reinsurance premium principle in the class is translation invariant or is the expected value principle, we show that a one-layer reinsurance treaty is optimal. Moreover, we use the expected value premium principle and Wang’s premium principle to demonstrate how the parameters in an optimal reinsurance treaty can be determined explicitly under a given premium principle.     

我国财产保险公司承保业务线经济资本的度量

承保风险是保险公司面临的主要风险之一,合理地计量其经济资本有助于提高公司的资本管理能力。采用多元Copula理论对我国某财险公司主要业务线的相依结构进行建模,选择拟合较好的GaussCopula,在此基础上,使用凹扭曲风险度量测度主要业务线的经济资本。结果显示:凹扭曲风险度量中的Wang风险度量能够根据风险的整体水平灵活地调整所需的经济资本。     

A general class of distortion operators for pricing contingent claims with applications to CAT bonds

ABSTRACT

The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the (Wang 2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g. skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.     

Optimal insurance in the presence of reinsurance

This paper studies an optimal insurance and reinsurance design problem among three agents: policyholder, insurer, and reinsurer. We assume that the preferences of the parties are given by distortion risk measures, which are equivalent to dual utilities. By maximizing the dual utility of the insurer and jointly solving the optimal insurance and reinsurance contracts, it is found that a layering insurance is optimal, with every layer being borne by one of the three agents. We also show that reinsurance encourages more insurance, and is welfare improving for the economy. Furthermore, it is optimal for the insurer to charge the maximum acceptable insurance premium to the policyholder. This paper also considers three other variants of the optimal insurance/reinsurance models. The first two variants impose a limit on the reinsurance premium so as to prevent insurer to reinsure all its risk. An optimal solution is still layering insurance, though the insurer will have to retain higher risk. Finally, we study the effect of competition by permitting the policyholder to insure its risk with an insurer, a reinsurer, or both. The competition from the reinsurer dampens the price at which an insurer could charge to the policyholder, although the optimal indemnities remain the same as the baseline model. The reinsurer will however not trade with the policyholder in this optimal solution.     

Time Varying Market Leverage, the Market Risk Premium and the Cost of Capital

This paper shows that, when as usual the market portfolio is proxied by a share portfolio, then the conventional Ibbotson (1999) estimator of the market risk premium violates Miller–Modigliani (1958 and 1963) propositions II and III. A new estimator of the market risk premium is proposed which is free of these defects. In addition, across the range of market leverages experienced in the US in the period 1952–1997, it generates estimates of the market risk premium that differ from those generated by the Ibbotson methodology by up to 2.5 percentage points, and weighted average costs of capital for firms that differ by up to 2.6 percentage points.     

Characterizations of optimal reinsurance treaties: a cost-benefit approach

This article investigates optimal reinsurance treaties minimizing an insurer’s risk-adjusted liability, which encompasses a risk margin quantified by distortion risk measures. Via the introduction of a transparent cost-benefit argument, we extend the results in Cui et al. [Cui, W., Yang, J. & Wu, L. (2013). Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles. Insurance: Mathematics and Economics 53, 74–85] and provide full characterizations on the set of optimal reinsurance treaties within the class of non-decreasing, 1-Lipschitz functions. Unlike conventional studies, our results address the issue of (non-)uniqueness of optimal solutions and indicate that ceded loss functions beyond the traditional insurance layers can be optimal in some cases. The usefulness of our novel cost-benefit approach is further demonstrated by readily solving the dual problem of minimizing the reinsurance premium while maintaining the risk-adjusted liability below a fixed tolerance level.     

Moments of renewal shot-noise processes and their applications

In this paper, we study the family of renewal shot-noise processes. The Feynmann–Kac formula is obtained based on the piecewise deterministic Markov process theory and the martingale methodology. We then derive the Laplace transforms of the conditional moments and asymptotic moments of the processes. In general, by inverting the Laplace transforms, the asymptotic moments and the first conditional moments can be derived explicitly; however, other conditional moments may need to be estimated numerically. As an example, we develop a very efficient and general algorithm of Monte Carlo exact simulation for estimating the second conditional moments. The results can be then easily transformed to the counterparts of discounted aggregate claims for insurance applications, and we apply the first two conditional moments for the actuarial net premium calculation. Similarly, they can also be applied to credit risk and reliability modelling. Numerical examples with four distribution choices for interarrival times are provided to illustrate how the models can be implemented.     

Litigation risk: Measurement and impact on M&A transaction terms

The purpose of the paper is to propose an original proprietary proxy of a firm's litigation risk. We extend the scope of litigation risk outside of the conflicts with shareholders and the domain of security litigation. We demonstrate that the source of the risk of litigation can be found in the firm's policies and in its management's operational or strategic decisions, even if a sector conditioning effect exists. Based on a sample of 465 US M&A transactions between 2000 and 2014, we provide evidence that the level of litigation risk, at the acquirer's level, has a positive and significant impact on the takeover premium. We also provide evidence that a significant relationship exists between the acquirer's litigation risk and the means of payment. An extension of the sample to international transactions is used as a robustness check; it confirms the previous results.     

Future Realized Return,Firm‐specific Risk and the Implied Expected Return

In this paper, I propose a novel approach to derive a firm‐specific measure of expected return. It builds on recent accounting‐based valuation models developed by Clubb (2013) and Ashton and Wang (2013). The measure is intrinsically linked to commonly used financial ratios, including book‐to‐market, (forward) earnings yield, and dividend‐to‐price, as well as growth and past returns. The empirical evidence shows that it is significantly positively associated with future realized stock returns and also significantly correlated with commonly used risk characteristics in a theoretically predictable manner. The results are likely to be of interest to practitioners and managers in making capital allocation decisions and to academics in need of proxies for firms’ discount rates and expected returns.     

会计信息失真现象的思考与探索

会计信息失真给社会的发展造成了极大的伤害,究其原因,有外部原因：政府监督的不到位,法律和会计监督体系的不健全;也有内部原因：会计从业人员个人和企业领导为个人利益和企业利益所驱动,以及会计人员的整体素质相对低下。本文在此基础上从完善法律体制、加强内外部监督力度、提高会计从业人员的整体素质等方面治理会计信息失真的措施,并提出实现会计信息化对治理会计信息失真是有着重大意义的。     

Relation between franking credits and the market risk premium: a comment

Based on the Officer (1994) model, Gray and Hall (2006) derive a relation between franking credits and the market risk premium. On the basis of this relation, the authors show that traditional estimates of the value of franking credits imply dividend yields that are inconsistent with historical equity market data. This inconsistency arises from assumptions about the franking credit payout ratio and the value of franking credits retained. With less than a 100 per cent payout ratio some franking credits are retained within the firm. Assuming that the retained franking credits have no value leads to the inconsistency in dividend yields. Current practice in the application of Officer's model makes this assumption and, therefore, leads to inconsistent results. Gray and Hall suggest resolving the inconsistency by setting the value of all franking credits to zero. An alternative solution is to recognize that retained franking credits might have a positive value.     

Inferring the Cost of Capital Using the Ohlson–Juettner Model

We compare risk premia (RP) inferred using the Ohlson-Juettner (RP_OJ) and residual income valuation (RP_RIV) models in three ways: (1) correlation with risk factors; (2) correlation with RP estimated by multiplying current realizations of risk factors by coefficients obtained from regressing prior-year RP on prior-year risk factors; and (3) correlation with ex post returns. RP_OJ has expected correlations with risk factors, a modest correlation with RP estimated from prior-year regressions, and an economically significant association with ex post returns. RP_RIV has generally higher correlations, but regression coefficients are sensitive to whether the industry median ROE is computed with or without loss firms.     

A Generalisation of the Mean-Variance Analysis

In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This 'mean-partial moments' utility generalises not only mean-variance utility of Tobin and Markowitz, but also mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker in this framework exhibits three types of aversions: aversion to loss, aversion to uncertainty in gains, and aversion to uncertainty in losses. Finally we present a solution to the optimal capital allocation problem and derive an expression for a portfolio performance measure which generalises the Sharpe and Sortino ratios. We demonstrate that in this framework the decision maker's skewness preferences have first-order impact on risk measurement even when the risk is small.     

Relationship between franking credits and the market risk premium

In a dividend imputation tax system, equity investors have three potential sources of return: dividends, capital gains and franking (tax) credits. However, the standard procedures for estimating the market risk premium (MRP) for use in the capital asset pricing model, ignore the value of franking credits. Officer (1994) notes that if franking credits do affect the corporate cost of capital, their value must be added to the standard estimates of MRP. In the present paper, we explicitly derive the relationship between the value of franking credits (gamma) and the MRP. We show that the standard parameter estimates that have been adopted in practice (especially by Australian regulators) violate this deterministic mathematical relationship. We also show how information on dividend yields and effective tax rates bounds the values that can be reasonably used for gamma and the MRP. We make recommendations for how estimates of the MRP should be adjusted to reflect the value of franking credits in an internally consistent manner.     

The impact of the euro on risk exposure of the world’s major banking industries

In this paper, we examine if the introduction of the euro impacted the risk exposures, risk premiums and, hence, the cost of equity of the banking industry of 11 Eurozone countries, five non-Eurozone European countries, and three non-European countries. Using a multi-factor asset-pricing model that allows time variation in the risk exposures, we find a statistically significant and economically large decline in the cost of equity of the banking industry across the three groups of countries following the introduction of the euro. Though we find an increase in the market and currency exposures after the euro, consistent with increased competition among banks, the fall in the cost of equity arises from an economically large decline in the currency premium. As expected, the Eurozone banking industry experienced the largest decrease. Our results are inconsistent with the argument that increased banking competition arising from the legislative changes accompanying the introduction of the euro would result in an increase in the overall risk premium of the banking sector.     

Relationship between franking credits and the market risk premium: a reply

We have previously documented an inconsistency between the dividend yield implied by the Officer (1994) model with standard Australian regulatory parameters and actual dividend yields of Australian companies. We have shown that, within the Officer framework, this inconsistency can be resolved by setting the assumed value of franking credits (γ) to zero, consistent with the practice of Australian firms and independent valuation experts. Truong and Partington (2008) and Lally (2008) recognize this same inconsistency and propose alternate ways of resolving it. In this paper, we demonstrate that these proposals are outside the Officer framework. The standard set of regulatory parameters cannot be resolved with observed dividend yields within the Officer framework. Whichever method is used to resolve the inconsistency, the effect will be an increase in the estimated after‐tax cost of equity.     

Optimal reinsurance arrangements in the presence of two reinsurers

In this paper, we investigate the optimal form of reinsurance from the perspective of an insurer when he decides to cede part of the loss to two reinsurers, where the first reinsurer calculates the premium by expected value principle while the premium principle adopted by the second reinsurer satisfies three axioms: distribution invariance, risk loading, and preserving stop-loss order. In order to exclude the moral hazard, a typical reinsurance treaty assumes that both the insurer and reinsurers are obligated to pay more for the larger loss. Under the criterion of minimizing value at risk (VaR) or conditional value at risk (CVaR) of the insurer's total risk exposure, we show that an optimal reinsurance policy is to cede two adjacent layers, where the upper layer is distributed to the first reinsurer. To further illustrate the applicability of our results, we derive explicitly the optimal layer reinsurance by assuming a generalized Wang's premium principle to the second reinsurer.     

Habit formation,the cross section of stock returns and the cash-flow risk puzzle

Non-linear external habit persistence models, which feature prominently in the recent “equity premium” asset pricing and macroeconomics literature, generate counterfactual predictions in the cross-section of stock returns. In particular, we show that in the absence of cross-sectional heterogeneity in firms’ cash-flow risk, these models produce a “growth premium,” that is, stocks with high price-to-fundamental ratios command a higher premium than stocks with low price-to-fundamental ratios. This implication is at odds with the well-established empirical observation of a “value premium” in the cross-section of stock returns. Substantial heterogeneity in firms’ cash-flow risk yields both a value premium as well as most of the stylized facts about the cross-section of stock returns, but it generates a “cash-flow risk puzzle”: Quantitatively, value stocks have to have “too much” cash-flow risk compared to the data to generate empirically plausible value premiums.     

Components of Market Risk and Return

This article proposes a flexible but parsimonious specificationof the joint dynamics of market risk and return to produce forecastsof a time-varying market equity premium. Our parsimonious volatilitymodel allows components to decay at different rates, generatesmean-reverting forecasts, and allows variance targeting. Thesefeatures contribute to realistic equity premium forecasts forthe U.S. market over the 1840–2006 period. For example,the premium forecast was low in the mid-1990s but has recentlyincreased. Although the market's total conditional variancehas a positive effect on returns, the smooth long-run componentof volatility is more important for capturing the dynamics ofthe premium. This result is robust to univariate specificationsthat condition on either levels or logs of past realized volatility(RV), as well as to a new bivariate model of returns and RV.