Surplus analysis for variable annuities with a GMDB option

In this paper, we analyze the insurance surplus for a Variable Annuity contract with a Guaranteed Minimum Death Benefit (GMDB) option. Initially, we derive the first two moments of the distribution of the surplus; and subsequently, we develop the whole distribution using a stochastic model which involves an integrated analysis of financial and mortality risk for a portfolio of annuities with GMDB embedded options. We offer a model according which the premium can be modified as per the forecasts of mortality probabilities, interest rate and fund evolution. Moreover, the study enables us to determine the premium that leads to a required probability of insolvency, and so it can be used for an evaluation of the adequacy of solvency. Numerical examples illustrate the results

Mortality risk and the valuation of annuities with guaranteed minimum death benefit options: application to the Italian population

In this note, we describe the payoff of Guaranteed Minimum Death Benefit options (GMDB) embedded in annuity contracts and discuss their valuation using data for the Italian male population as a case study. These put options have stochastic maturity dates due to the involuntary exercise at the moment of death. We value the GMDB as a weighted average price of a set of deterministic put options with different maturity dates, where the weights are the probability of death at every date. We take into account the mortality risk and investigate the sensitivity of the price of the option to changes in mortality probability using both deterministic and stochastic approaches

Effect of Relationship Quality and Cost to Serve on Customer Value in Business Market

Traditionally, marketers have assumed that investing in the quality of relationships with customers would generate superior profitability to the selling firm. The assumption is that coordination and collaboration between buyer and seller create value for both firms by reducing costs and expanding revenue opportunities. However, such value creation mechanism does not work every time. Closer relationships require customer specific investments and a higher level of service that may create more cost to the seller than the potential gain in revenue, negatively impacting profitability of the selling firm. This research explores the effect of buyer-seller relationship quality on value creation for the selling firm, emphasizing the understanding of costs associated with serving the relationship. Two studies were conducted: Study 1 qualitatively examines the cost associated with serving customers and estimates actual cost-to-serve for individual customers. Study 2 measures the quality of customer relationships, past customer profitability and customer lifetime value for each customer relationship in the proposed sample. Finally, the effect of RQ on customer lifetime value is evaluated. Results suggest that investing in customer relationships have an effect on the drivers of customer cost and profitability. However, the net effect on customer value is not as clear as it depends on the trade offs of the different drivers of cost and profit

Evaluating the Effect of Deposition Strategy on Mechanical Characteristics of 316L Parts Produced by Laser Powder Directed Energy Deposition Process

The production of large components, the possibility to repair damaged parts and the ability to produce components of multi-graded or functional-graded materials are the main drivers of the research and the application of the Laser Powder Directed Energy Deposition (LP-DED) process. However, the knowledge of the process and of the relationships among the process parameters and the characteristics of the produced part is currently not completely understood. The aim of this paper is to fill the current gap in the scientific literature related to the effect of the deposition strategy on the part quality. Therefore, the influence of two of the most important parameters, namely the deposition path and the idle time, on the residual stresses and porosity is evaluated on 316L samples produced by the LP-DED process. The obtained results show that both parameters have a high influence on the porosity level and the residual stresses. In particular, it can be seen that a high value of idle time worsens both porosity and residual stresses. Then, it is also observed that the raster deposition path leads to a lower value of stresses

COVID-19 crisis and resilience: challenges for the insurance sector

The main role of the insurance sector is the coverage of risks through pooling techniques. Against the payment of a premium, the insurance company compensates for unexpected losses, including catastrophic events and pandemics. However, differently from a catastrophic event, the COVID-19 pandemic has highlighted that the global impact on economic and financial activities is highly correlated. The insurance sector itself has been strongly affected both by the exponential growth of claims in the life and non-life sectors and by the negative impact on financial activities. Past experiences in pandemic risk management have been unsuccessful. This paper retraces the instruments issued following the past pandemics and tries to reflect on how the insurance sector can implement innovative solutions to support post-pandemic resilience

Efficient audit strategies for defined benefit pension plans

The aim of this paper is to describe efficient audit strategies for the the risk management of defined benefit pension plans

The dependency premium based on a multifactor model for dependent mortality data

As shown in the literature, the dependence structure in mortality data cannot be ignored in projecting future trends, in particular for a group of similar populations characterized by common long run relationships. We propose a new multifactor model for capturing common and specific features of the trend over time. We implement the model and investigate its impact on actuarial valuations, through the introduction of the concept of the dependency premium

Influence of High-Productivity Process Parameters on the Surface Quality and Residual Stress State of AISI 316L Components Produced by Directed Energy Deposition

The production of large components is one of the most powerful applications of laser powder-directed energy deposition (LP-DED) processes. High productivity could be achieved, when focusing on industrial applications, by selecting the proper process parameters. However, it is of crucial importance to understand the strategies that are necessary to increase productivity while maintaining the overall part quality and minimizing the need for post-processing. In this paper, an analysis of the dimensional deviations, surface roughness and subsurface residual stresses of samples produced by LP-DED is described as a function of the applied energy input. The aim of this work is to analyze the effects of high-productivity process parameters on the surface quality and the mechanical characteristics of the samples. The obtained results show that the analyzed process parameters affect the dimensional deviations and the residual stresses, but have a very little influence on surface roughness, which is instead dominated by the presence of unmelted particles

On the quality of unsupported overhangs produced by laser powder bed fusion

One of the main design constraints for additive manufacturing is the definition of downward-facing surfaces, which can lead to problems, like part failing or warping, during construction and poor surface quality. In this paper, a specific index has been defined to represent the surface quality of the downward-facing surfaces induced by the laser powder bed fusion (L-PBF) process. In order to validate the quality index, a design of experiment (DoE) that considers geometric parameters of the overhangs has been defined and carried out, and the quality of resulting surfaces has been evaluated using an optical scanning system. The statistical analysis (ANOVA) has allowed identifying the relationships between significant geometrical parameters and the quality index here proposed