Expected Value Premium Research Articles

Measuring Risk When Expected Losses Are Unbounded

This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial applications are analyzed, such as extensions of the expected value premium principle when expected losses are unbounded.

Optimal reinsurance under distortion risk measures and expected value premium principle for reinsurer

This paper discusses optimal reinsurance strategy by minimizing insurer’s risk under one general risk measure: Distortion risk measure. The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss. An explicit solution of the insurer’s optimal reinsurance problem is obtained. The optimal strategies for some special distortion risk measures, such as value-at-risk (VaR) and tail value-at-risk (TVaR), are also investigated.

Optimal Dynamic Risk Control for Insurers with State-Dependent Income

In this paper we investigate optimal forms of dynamic reinsurance polices among a class of general reinsurance strategies. The original surplus process of an insurance portfolio is assumed to follow a Markov jump process with state-dependent income. We assume that the insurer uses a dynamic reinsurance policy to minimize the probability of absolute ruin, where the traditional ruin can be viewed as a special case of absolute ruin. In terms of approximation theory of stochastic process, the controlled diffusion model with a general reinsurance policy is established strictly. In such a risk model, absolute ruin is said to occur when the drift coefficient of the surplus process turns negative, when the insurer has no profitability any more. Under the expected value premium principle, we rigorously prove that a dynamic excess-of-loss reinsurance is the optimal form of reinsurance among a class of general reinsurance strategies in a dynamic control framework. Moreover, by solving the Hamilton-Jacobi-Bellman equation, we derive both the explicit expression of the optimal dynamic excess-of-loss reinsurance strategy and the closed-form solution to the absolute ruin probability under the optimal reinsurance strategy. We also illustrate these explicit solutions using numerical examples.

Optimal Dynamic Risk Control for Insurers with State-Dependent Income

In this paper we investigate optimal forms of dynamic reinsurance polices among a class of general reinsurance strategies. The original surplus process of an insurance portfolio is assumed to follow a Markov jump process with state-dependent income. We assume that the insurer uses a dynamic reinsurance policy to minimize the probability of absolute ruin, where the traditional ruin can be viewed as a special case of absolute ruin. In terms of approximation theory of stochastic process, the controlled diffusion model with a general reinsurance policy is established strictly. In such a risk model, absolute ruin is said to occur when the drift coefficient of the surplus process turns negative, when the insurer has no profitability any more. Under the expected value premium principle, we rigorously prove that a dynamic excess-of-loss reinsurance is the optimal form of reinsurance among a class of general reinsurance strategies in a dynamic control framework. Moreover, by solving the Hamilton-Jacobi-Bellman equation, we derive both the explicit expression of the optimal dynamic excess-of-loss reinsurance strategy and the closed-form solution to the absolute ruin probability under the optimal reinsurance strategy. We also illustrate these explicit solutions using numerical examples.

Optimal Dynamic Risk Control for Insurers with State-Dependent Income

In this paper we investigate optimal forms of dynamic reinsurance polices among a class of general reinsurance strategies. The original surplus process of an insurance portfolio is assumed to follow a Markov jump process with state-dependent income. We assume that the insurer uses a dynamic reinsurance policy to minimize the probability of absolute ruin, where the traditional ruin can be viewed as a special case of absolute ruin. In terms of approximation theory of stochastic process, the controlled diffusion model with a general reinsurance policy is established strictly. In such a risk model, absolute ruin is said to occur when the drift coefficient of the surplus process turns negative, when the insurer has no profitability any more. Under the expected value premium principle, we rigorously prove that a dynamic excess-of-loss reinsurance is the optimal form of reinsurance among a class of general reinsurance strategies in a dynamic control framework. Moreover, by solving the Hamilton-Jacobi-Bellman equation, we derive both the explicit expression of the optimal dynamic excess-of-loss reinsurance strategy and the closed-form solution to the absolute ruin probability under the optimal reinsurance strategy. We also illustrate these explicit solutions using numerical examples.

OPTIMAL REINSURANCE WITH LIMITED CEDED RISK: A STOCHASTIC DOMINANCE APPROACH

AbstractAn optimal reinsurance problem from the perspective of an insurer is studied in this paper, where an upper limit is imposed on a reinsurer's expected loss over a prescribed level. In order to reduce the moral hazard, we assume that both the insurer and the reinsurer are obligated to pay more as the amount of loss increases in a typical reinsurance treaty. We further assume that the optimization criterion preserves the convex order. Such a criterion is very general as most of the criteria for optimal reinsurance problems in the literature preserve the convex order. When the reinsurance premium is calculated as a function of the actuarial value of coverage, we show via a stochastic dominance approach that any admissible reinsurance policy is dominated by a stop-loss reinsurance or a two-layer reinsurance, depending upon the amount of the reinsurance premium. Moreover, we obtain a similar result to Mossin's Theorem and find that it is optimal for the insurer to cede a loss as much as possible under the net premium principle. To further examine the reinsurance premium for the optimal piecewise linear reinsurance policy, we assume the expected value premium principle and derive the optimal reinsurance explicitly under (1) the criterion of minimizing the variance of the insurer's risk exposure, and (2) the criterion of minimizing the risk-adjusted value of the insurer's liability where the liability valuation is carried out using the cost-of-capital approach based on the conditional value at risk.

Value versus Growth: Time‐Varying Expected Stock Returns

Is the value premium predictable? We study time variations of the expected value premium using a two‐state Markov switching model. We find that when conditional volatilities are high, the expected excess returns of value stocks are more sensitive to aggregate economic conditions than the expected excess returns of growth stocks. As a result, the expected value premium is time varying. It spikes upward in the high volatility state, only to decline more gradually in the subsequent periods. However, out‐of‐sample predictability of the value premium is close to nonexistent.

Value Versus Growth: Time-Varying Expected Stock Returns

Using the Markov switching framework of Perez-Quiros and Timmermann (2000), we show that the expected value-minus-growth returns display strong countercyclical variations. Under a variety of flexibility proxies such as the ratio of fixed assets to total assets, the frequency of disinvestment, financial leverage, and operating leverage, we show that value firms are less flexible in adjusting to worsening economic conditions than growth firms, and that inflexibility increases the costs of equity in the cross section. The time-variation in the expected value premium highlights the importance of conditioning information in understanding the cross section of average returns.

Expected returns on value, growth, and HML

Abstract In this paper, I analyze the predictability of returns on value and growth portfolios and examine time variation of the expected value premium. As a primary tool, I use the filtering technique, which accounts for time variation in expected cash flows and explicitly exploits the constraints imposed by the present value relation. I demonstrate that returns on value and growth portfolios are predictable, and the predictability is stronger for growth stocks. Applying the filtering technique to the HML portfolio, I build a novel powerful forecaster for the value premium. The new forecaster appears to be only weakly related to business cycle variables.

Style Timing with Insiders

Aggregate demand by insiders predicts time-series variation in the value premium — between 1978 and 2004, a one standard deviation increase in aggregate insider demand in the previous six months forecasts a 53 basis point decline (6.54% annualized) in the expected value premium in the month following publication of the insider trading data. Further tests suggest that insider trading forecasts the value premium because insiders trade against systematic investor sentiment-induced mispricing and growth stocks are more sensitive to changes in sentiment than value stocks, i.e., insiders sell (buy) when markets, and growth stocks especially, are overvalued (undervalued). As a result, our analysis suggests that investors can use signals from aggregate insider behavior to adjust style tilts and exploit sentiment-induced mispricing.

The expected value premium

Fama and French [2002. The equity premium. Journal of Finance 57, 637–659] estimate the equity premium using dividend growth rates to measure expected rates of capital gain. We apply their method to study the value premium. From 1945 to 2005, the expected value premium is on average 6.1% per annum, consisting of an expected dividend growth component of 4.4% and an expected dividend price ratio component of 1.7%. Unlike the equity premium, the value premium has been largely stable over the last half century.

The Expected Value Premium

Fama and French (2002) estimate the equity premium using dividend growth rates to measure expected rates of capital gain. We use a similar method to study the value premium. From 1941 to 2005, the expected HML return is on average 6.0% per annum, consisting of an expected dividend-growth component of 4.4% and an expected dividend-price-ratio component of 1.6%. The expected HML return is also countercyclical: a positive, one-standard-deviation shock to real consumption growth lowers this premium by about 0.40%. Unlike the equity premium, there is only mixed evidence suggesting that the expected value premium has declined over time.