Dual characterization of properties of risk measures on Orlicz hearts

We extend earlier representation results for monetary risk measures on Orlicz hearts. Then we give general conditions for such risk measures to be Gateaux-differentiable, strictly monotone with respect to almost sure inequality, strictly convex modulo translation, strictly convex modulo comonotonicity, or monotone with respect to different stochastic orders. The theoretical results are used to analyze various specific examples of risk measures. We thank Andreas Hamel and Michael Kupper for fruitful discussions and helpful comments. P. Cheridito has been supported by NSF Grant DMS-0642361, a Rheinstein Award and a Peek Fellowship. T. Li has been supported by a Marshall Scholarship and a Merage Fellowship.     

Sample path large and moderate deviations for risk model with delayed claims

Sample path large and moderate deviation principles for Markov modulated risk models with delayed claims are proved by the exponential martingale method. As applications, asymptotic estimates and exponential bounds of the ruin probability are also studied.     

Recent applications of theory of the firm under uncertainty

This paper provides a comprehensive synthesis and analysis of the current and recent empirical implementations of the theory of the firm under uncertainty, including multiple sources of uncertainty. In so doing, it identifies the major estimation obstacles and it offers the future empirical researcher ways to derive simple estimation procedures under multiple sources uncertainty.     

Using a risk-based approach to project scheduling: A case illustration from semiconductor manufacturing

This paper introduces a risk-based optimization method to schedule projects. The method uses risk mitigation and optimal control techniques to minimize variables such as the project duration or the cost estimate at completion. Mitigation actions reduce the risk impacts that may affect the system. A model predictive control approach is used to determine the set of mitigation actions to be executed and the time in which they are taken. A real-life project in the field of semiconductor manufacturing has been taken as an example to show the benefits of the method in a deterministic case and a Monte Carlo simulation has also been carried out.     

Constant dividend barrier in a risk model with interclaim-dependent claim sizes

The risk model with interclaim-dependent claim sizes proposed by Boudreault et al. [Boudreault, M., Cossette, H., Landriault, D., Marceau, E., 2006. On a risk model with dependence between interclaim arrivals and claim sizes. Scand. Actur. J., 265-285] is studied in the presence of a constant dividend barrier. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber-Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Finally, we analyze the expected present value of dividend payments before ruin in the same class of risk models. An homogeneous integro-differential equation is derived and then solved. Its solution can be expressed as a different combination of the two fundamental solutions to the homogeneous integro-differential equation associated to the Gerber-Shiu discounted penalty function.     

Applications of a multi-state risk factor/mortality model in life insurance

Mortality rates are known to depend on socio-economic and behavioral risk factors, and actuarial calculations for life insurance policies usually reflect this. It is typically assumed, however, that these risk factors are observed only at policy issue, and the impact of changes that occur later is not considered. In this paper, we present a discrete-time, multi-state model for risk factor changes and mortality. It allows one to more accurately describe mortality dynamics and quantify variability in mortality. This model is extended to reflect health status and then used to analyze the impact of selective lapsation of life insurance policies and to predict mortality under reentry term insurance.     

Risk estimation of infectious diseases determines the effectiveness of the control strategy

Usually, whether to take vaccination or not is a voluntary decision, which is determined by many factors, from societal factors (such as religious belief and human rights) to individual preferences (including psychology and altruism). Facing the outbreaks of infectious diseases, different people often have different estimations on the risk of infectious diseases. So, some persons are willing to vaccinate, but other persons are willing to take risks. In this paper, we establish two different risk assessment systems using the technique of dynamic programming, and then compare the effects of the two different systems on the prevention of diseases on complex networks. One is that the perceived probability of being infected for each individual is the same (uniform case). The other is that the perceived probability of being infected is positively correlated to individual degrees (preferential case). We show that these two risk assessment systems can yield completely different results, such as, the effectiveness of controlling diseases, the time evolution of the number of infections, and so on.     

First- and second-price sealed-bid auctions applied to push and pull supply contracts

We investigate a newsvendor-type retailer sourcing problem under demand uncertainty who has the option to source from multiple suppliers. The suppliers’ manufacturing costs are private information. A widely used mechanism to find the least costly supplier under asymmetric information is to use a sealed-bid reverse auction. We compare the combinations of different simple auction formats (first- and second-price) and risk sharing supply contracts (push and pull) under full contract compliance, both for risk-neutral and risk-averse retailer and suppliers. We show the superiority of a first-price push auction for a risk-neutral retailer. However, only the pull contracts lead to supply chain coordination. If the retailer is sufficiently risk-averse, the pull is preferred over the push contract. If suppliers are risk-averse, the first-price push auction remains the choice for the retailer. Numerical examples illustrate the allocation of benefits between the retailer and the (winning) supplier for different number of bidders, demand uncertainty, cost uncertainty, and degree of risk-aversion.     

More than a second channel? Supply chain strategies in B2B spot markets

The emergence of B2B spot markets has greatly facilitated spot trading and impacted supply chain structures as well as the way commercial transactions take place between firms in many industries. While providing new opportunities, the B2B spot market also exposes participants to a price risk. This new business landscape raises some important questions on how the supplier and manufacturer should change their sales channel and procurement strategies and tailor their decisions to this changing environment. In this paper, we study the channel-choice, pricing and ordering/production decisions of the risk-averse supplier and manufacturer in a two-tier supply chain with a B2B spot market. Our analysis shows that, to benefit from the B2B spot market and control the risk exposure, the upstream supplier should develop an integrated channel-choice and pricing strategy. When the supplier adopts a dual-channel strategy, the equilibrium contract price decreases in the supplier’s risk attitude, but increases in the demand uncertainty. However, it first decreases and then increases in the manufacturer’s risk attitude and spot price volatility. We conclude that rather than simply being a second channel, the B2B spot market provides a strategic tool to supply chain members to achieve an advantageous position in their contract trading.     

A separation theorem for the weak s-convex orders

The present paper extends to higher degrees the well-known separation theorem decomposing a shift in the increasing convex order into a combination of a shift in the usual stochastic order followed by another shift in the convex order. An application in decision making under risk is provided to illustrate the interest of the result.