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In this paper, we study the so-called "wrong skewness" anomaly in Stochastic Frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error. We propose a more general and flexible specification of the SF model, introducing dependence between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error in three components, namely: i) the asymmetry of the inefficiency term; ii) the asymmetry of the random error; and iii) the structure of dependence between the error components. This decomposition suggests that the "wrong skewness"anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign.We present two empirical applications. In the first dataset, where the classic SF displays wrong skewness, estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error.In the second dataset, where the classic SF does not display any anomaly, estimation of our model provides evidence of the presence of both dependence between the error components and asymmetry of the random error.

Life insurance products are usually equipped with minimum guarantee and bonus provision options. The pricing of such claims is of vital importance for the insurance industry. Risk management, strategic asset allocation, and product design depend on the correct evaluation of the written options. Also regulators are interested in such issues since they have to be aware of the possible scenarios that the overall industry will face. Pricing techniques based on the Black & Scholes paradigm are often used, however, the hypotheses underneath this model are rarely met.To overcome Black & Scholes limitations, we develop a stochastic programming model to determine the fair price of the minimum guarantee and bonus provision options. We show that such a model covers the most relevant sources of incompleteness accounted in the financial and insurance literature. We provide extensive empirical analyses to highlight the effect of incompleteness on the fair value of the option, and show how the whole framework can be used as a valuable normative tool for insurance companies and regulators.

The article studies the valuation and optimal management of Time Charters with Purchase Options (T/C-POPs), which is a specific type of asset lease with embedded options that is common in shipping markets. T/C-POPs are economically significant and sometimes account for more than half of the stock market value of listed shipping companies. The main source of risk in markets for maritime transportation is the freight rate, and we therefore specify a single-factor continuous time model for the dynamic evolution of freight rates that allows us to price a wide variety of freight rate-related derivatives including various forms of T/C-POPs using contingent claims valuation techniques. Our model allows for the derivation of closed valuation formulas for some simple freight rate derivatives, whereas the more complex ones are analysed using numerical (finite difference) procedures. We accompany our theoretical results with illustrative numerical examples as we proceed.Ship valuation, options on ships, leasing, lease contracts with options, optimal stopping,