Optimal Reciprocal Reinsurance Treaties Under the Joint Survival Probability and the Joint Profitable Probability

A reinsurance treaty involves two parties, an insurer and a reinsurer. The two parties have conflicting interests. Most existing optimal reinsurance treaties only consider the interest of one party. In this article, we consider the interests of both insurers and reinsurers and study the joint survival and profitable probabilities of insurers and reinsurers. We design the optimal reinsurance contracts that maximize the joint survival probability and the joint profitable probability. We first establish sufficient and necessary conditions for the existence of the optimal reinsurance retentions for the quota‐share reinsurance and the stop‐loss reinsurance under expected value reinsurance premium principle. We then derive sufficient conditions for the existence of the optimal reinsurance treaties in a wide class of reinsurance policies and under a general reinsurance premium principle. These conditions enable one to design optimal reinsurance contracts in different forms and under different premium principles. As applications, we design an optimal reinsurance contract in the form of a quota‐share reinsurance under the variance principle and an optimal reinsurance treaty in the form of a limited stop‐loss reinsurance under the expected value principle.     

Offshoring Quotas and Strategic Export Subsidies

We present an analysis of strategic export subsidization in the presence of exogenous limits on the extent of offshoring that is permissible for a domestic firm. Rather than offsetting a quota’s cost-raising effect, the government reduces its optimal strategic subsidy compounding the negative effects on the domestic firm’s market share. This double jeopardy of lower subsidies and greater offshoring restrictions must reduce domestic profits as well as domestic welfare. Finally, we show that there is no guarantee that such an offshoring quota will raise domestic employment in the oligopolistic sector, calling into question the efficacy of such a barrier.     

Optimal retention levels,given the joint survival of cedent and reinsurer

A certain volume of risks is insured and there is a reinsurance contract, according to which claims and total premium income are shared between a direct insurer and a reinsurer in such a way, that the finite horizon probability of their joint survival is maximized. An explicit expression for the latter probability, under an excess of loss (XL) treaty is derived, using the improved version of the Ignatov and Kaishev's ruin probability formula (see Ignatov, Kaishev & Krachunov. 2001a) and assuming, Poisson claim arrivals, any discrete joint distribution of the claims, and any increasing real premium income function. An explicit expression for the probability of survival of the cedent only, under an XL contract is also derived and used to determine the probability of survival of the reinsurer, given survival of the cedent. The absolute value of the difference between the probability of survival of the cedent and the probability of survival of the reinsurer, given survival of the cedent is used for the choice of optimal retention level. We derive formulae for the expected profit of the cedent and of the reinsurer, given their joint survival up to the finite time horizon. We illustrate how optimal retention levels can be set, using an optimality criterion based on the expected profit formulae. The quota share contract is also considered under the same model. It is shown that the probability of joint survival of the cedent and the reinsurer coincides with the probability of survival of solely the insurer. Extensive, numerical comparisons, illustrating the performance of the proposed reinsurance optimality criteria are presented.     

VAR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance

Abstract

It is well known that reinsurance can be an effective risk management tool for an insurer to minimize its exposure to risk. In this paper we provide further analysis on two optimal reinsurance models recently proposed by Cai and Tan. These models have several appealing features including (1) practicality in that the models could be of interest to insurers and reinsurers, (2) simplicity in that optimal solutions can be derived in many cases, and (3) integration between banks and insurance companies in that the models exploit explicitly some of the popular risk measures such as value-at-risk and conditional tail expectation. The objective of the paper is to study and analyze the optimal reinsurance designs associated with two of the most common reinsurance contracts: the quota share and the stop loss. Furthermore, as many as 17 reinsurance premium principles are investigated. This paper also highlights the critical role of the reinsurance premium principles in the sense that, depending on the chosen principles, optimal quota-share and stop-loss reinsurance may or may not exist. For some cases we formally establish the sufficient and necessary (or just sufficient) conditions for the existence of the nontrivial optimal reinsurance. Numerical examples are presented to illustrate our results.     

Sharing Risk with the Government: How Taxes Affect Corporate Risk Taking

Using 113 staggered changes in corporate income tax rates across U.S. states, we provide evidence on how taxes affect corporate risk‐taking decisions. Higher taxes reduce expected profits more for risky projects than for safe ones, as the government shares in a firm's upside but not in its downside. Consistent with this prediction, we find that risk taking is sensitive to taxes, albeit asymmetrically: the average firm reduces risk in response to a tax increase (primarily by changing its operating cycle and reducing R&D risk) but does not respond to a tax cut. We trace the asymmetry back to constraints on risk taking imposed by creditors. Finally, tax loss‐offset rules moderate firms’ sensitivity to taxes by allowing firms to partly share downside risk with the government.     

DESIGNING CAPITAL STRUCTURE TO CREATE SHAREHOLDER VALUE

In the past decade, many U.S. companies have launched aggressive share repurchase programs with the expectation that value can be created by returning excess capital to shareholders and moving the firm closer to its optimal capital structure. But how much capital does a company really need to support its business activities? This article presents an economic framework or “model” that can be used to simulate the effect of various capital structure choices on shareholder value. The fundamental insight underlying the model is that judicious use of debt can add value by reducing corporate taxes and strengthening management incentives to increase efficiency, but that too much debt can result in a loss of business and perhaps a costly reorganization. Indeed, one of the key findings of the authors' recent research is that companies with highly leveraged balance sheets suffer disproportionately large losses in market share and value during industry downturns. As illustrated in a case study of a hypothetical general merchandiser, the model makes it possible to identify an optimal debt-equity ratio (and percentage of fixed- versus floating-rate debt)—one that balances the value of the tax shield from debt against the increased risk of financial distress.     

Ownership Restrictions and Stock Prices: Evidence from Chinese Markets

In this paper, I test a one-period capital asset pricing model (CAPM) under share ownership restrictions to explain differences in prices and expected excess returns between the classes of shares that can be bought and traded by domestic and foreign investors, respectively, in the Chinese stock markets. I find that cross-sectional variability in the spread between the expected domestic and foreign share excess returns is related to differences in individual shares' market betas. The empirical results are by and large consistent with the CAPM. After the betas are controlled for, idiosyncratic variance and firm size have no effect.     

Equilibrium in Competitive Insurance Markets Under Adverse Selection and Yaari's Dual Theory of Risk

Under Yaari's dual theory of risk, we determine the equilibrium separating contracts for high and low risks in a competitive insurance market, in which risks are defined only by their expected losses, that is, a high risk is a risk that has a greater expected loss than a low risk. Also, we determine the pooling equilibrium contract when insurers are assumed non-myopic. Expected utility theory generally predicts that optimal insurance indemnity payments are nonlinear functions of the underlying loss due to the nonlinearity of agents' utility functions. Under Yaari's dual theory, we show that under mild technical conditions the indemnity payment is a piecewise linear function of the loss, a common property of insurance coverages.     

The predictability of returns on equity REITs and their co-movement with other assets

Recent evidence suggests that the variation in the expected excess returns is predictable and arises from changes in business conditions. Using a multifactor latent variable model with time-varying risk premiums, we decompose excess returns into expected and unexpected excess returns to examine what determines movements in expected excess returns for equity REITs are more predictable than all other assets examined, due in part to cap rates which contain useful information about the general risk condition in the economy. We also find that the conditional risk premiums (expected excess returns) on EREITs move very closely with those of small cap stocks and much less with those of bonds.     

Reinsurance Arrangements Maximizing Insurer's Survival Probability

The article concerns the problem of purchasing a reinsurance policy that maximizes the survival probability of the insurer. Explicit forms of the contracts optimal for the insurer are derived which are stop loss or truncated stop loss depending on the initial surplus, a quota to be spend on reinsurance and pricing rules of both the insurer and the reinsurer.     

Double signals or single signal? An investigation of insider trading around share repurchases

We examine directors’ dealing activity around share repurchasing periods in Hong Kong. There are significant insider trading activities before the share repurchasing period. Consistent with the signaling hypothesis, the directors’ purchase activities during the share repurchase period are significantly higher than the expected level while the directors’ sale activities are significantly lower than the expected level. Double signals of share repurchase and directors’ purchases create a stronger signal in conveying undervaluation, while insider sales around share repurchase reduces the undervaluation signal. We find some evidence that is consistent with the free cash flow and signaling arguments for share repurchases.     

On the optimality of proportional reinsurance

Proportional reinsurance is often thought to be a very simple method of covering the portfolio of an insurer. Theoreticians are not really interested in analysing the optimality properties of these types of reinsurance covers. In this paper, we will use a real-life insurance portfolio in order to compare four proportional structures: quota share reinsurance, variable quota share reinsurance, surplus reinsurance and surplus reinsurance with a table of lines.     

Optimal reinsurance under general law-invariant risk measures

In recent years, general risk measures play an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance decision problems using risk measures beyond the classical expected utility framework. In this paper, we first show that the stop-loss reinsurance is an optimal contract under law-invariant convex risk measures via a new simple geometric argument. A similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution. These two results highlight that law-invariant convex risk measure is better and more robust, in the sense that the corresponding optimal reinsurance still provides the protection coverage against extreme loss irrespective to the potential increment of its probability of occurrence, to expected larger claim than Value at Risk and Conditional Tail Expectation which are more commonly used. Several illustrative examples will be provided.     

Pricing for Multiline Insurer: Frictional Costs,Insolvency, and Asset Allocation

This article examines multiline insurance pricing based on the contingent claim approach in a limited liability and frictional costs environment. Capital allocation is based on the value of the default option, which satisfies the realistic assumption that each distinct line undertakes a pro rata share of deficit caused by insurer insolvency. Premium levels, available assets, and default risk interact with each other and reach equilibrium at the fair premium. The assets available to pay for liabilities are not predetermined or given; instead, the premium income and investment income jointly influence the available assets. The results show that equity allocation does not influence the overall fair premium. For a given expected loss, the premium-to-expected-loss ratio for firms offering multiple lines is higher than that for firms only offering a single line, due to the reduced risk achieved through diversification. Premium-to-expected-loss ratio and equity-to-expected-loss ratio vary across lines. Lines having a higher possibility or claim amount not being paid in full exhibit lower premium-to-expected-loss ratio and higher equity-to-expected-loss ratio. Positive correlation among lines of business results in lower premium-to-expected-loss ratio than when independent losses are assumed. Positive correlation between investment return and losses reduces the insolvency risk and leads to a higher premium-to-expected-loss ratio.     

Pension Benefit Security: A Comparison of Solvency Requirements,a Pension Guarantee Fund,and Sponsor Support

Developed countries apply different security mechanisms in regulation to protect pension benefits: solvency requirements, a pension guarantee fund (PGF), and sponsor support. We compare these mechanisms for a generalized form of hybrid pension schemes. We calculate the expected log return for the beneficiaries, the shortfall probability, that is, the likelihood of the pension payment falling below the promised level and the expected loss given shortfall. Comparing solvency requirements to a pension guarantee system or sponsor support involves trading off risk and return. Additional spending on default insurance reduces the shortfall probability and the expected loss given shortfall but also lowers the probability of high positive returns as are feasible under solvency requirements.     

ESTIMATING EXPECTED EXCESS RETURNS USING HISTORICAL AND OPTION‐IMPLIED VOLATILITY

We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003 using the proportional reward‐to‐risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and realized excess returns. In contrast, when risk is measured by option‐implied volatility, we find a positive and significant relation between expected and realized excess returns in the 1994–1998 subperiod. In the 1999–2003 subperiod, the option‐implied volatility risk measure yields a positive, but statistically insignificant, risk‐return relation. We attribute this performance difference to the fact that, in the 1994–1998 subperiod, return volatility was lower and the average return was much higher than in the 1999–2003 subperiod, thereby increasing the signal‐to‐noise ratio in the latter subperiod.     

A mean/variance approach to long-term fixed-income portfolio allocation

Abstract

Long-term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default spread, measuring the difference between the yield when no default occurs and the expected yield. For zero-coupon bonds and for actual market data, the default spread is proportional to the probability of default per year. The analysis of market data shows that the yield spread scales as the square root of the default spread. This relation expresses the risk premium over the risk-free rate that the bond market offers, similarly to the risk premium for equities. With these measures for risk and return, an optimal bond allocation scheme can be built following a mean/variance utility function. Straightforward computations allow us to obtain the optimal portfolio, depending on a pre-set risk-aversion level. As for equities, the optimal portfolio is a linear combination of one risk-free bond and a risky portfolio. Using the scaling law for the default spread allows us to obtain simple expressions for the value, yield and risk of the optimal portfolio.     

Time Variation in the Covariance between Stock Returns and Consumption Growth

The conditional covariance between aggregate stock returns and aggregate consumption growth varies substantially over time. When stock market wealth is high relative to consumption, both the conditional covariance and correlation are high. This pattern is consistent with the “composition effect,” where agents' consumption growth is more closely tied to stock returns when stock wealth is a larger share of total wealth. This variation can be used to test asset‐pricing models in which the price of consumption risk varies. After accounting for variations in this price, the relation between expected excess stock returns and the conditional covariance is negative.     

Chinese IPO activity,pricing, and market cycles

We examine the activity, pricing, and market cycles of 1,380 Chinese A share IPOs over the period 1991–2005 and find initial underpricing of 238%. The government restrictions on IPO offer price and quota allocation cause pricing structural breaks and attribute more than half of initial underpricing. A multifactor model that includes firm’s characteristics, excess demand for IPO shares, and the government restrictions explains cross-sectional initial returns, after controlling for industrial differences and stock market conditions. In addition, monthly IPO volume and average initial return are highly correlated. A VAR model indicates that initial return leads IPO volume by 6 months.     

Dynamic portfolio strategy by loss-averse fund managers facing performance-induced fund flows

In a continuous-time framework, we establish an optimal dynamic portfolio strategy for a loss-averse fund manager facing performance-induced fund flows. Using the martingale approach, we derive closed-form solutions to both the optimal terminal value and optimal dynamic strategy of the fund under management. The model shows that the loss-averse manager strives to earn high returns in good market conditions at the risk of losing all investments at the terminal date in bad market conditions. The prospect of higher fund inflows induced by superior performance motivates fund managers to take more aggressive investment strategies, increasing the fund's risk exposure, whereas the prospect of fund outflows due to underperformance has no impact on the fund manager's investment decision. While the prospect of higher fund inflows increases dynamic optimal wealth as well as optimal terminal wealth in good market conditions, in bad market conditions, it reduces dynamic optimal wealth and results in a higher chance of a complete loss at the terminal date. Finally, a manager with a higher degree of loss aversion tends to take a conservative investment strategy with a lower risk exposure especially in bad market conditions, leading to a lower dynamic and terminal wealth in good market conditions and also a lower chance of a complete loss in bad market conditions.