We study the design of optimal insurance contracts when the insurer can default on its obligations. In our model default arises endogenously from the interaction of the insurance premium, the indemnity schedule and the insurer's assets. This allows us to understand the joint effect of insolvency...

The purpose of this paper is to conduct a market-consistent valuation of life insurance participating liabilities sold to a population of partially heterogeneous customers under the joint impact of biometric and financial risk. In particular, the heterogeneity between groups of policyholders...

In a quantitative model with uncertain inputs, the uncertainty of the output can be summarized by a risk measure. We propose a sensitivity analysis method based on derivatives of the output risk measure, in the direction of model inputs. This produces a global sensitivity measure, explicitly...

Life annuities and pension products usually involve a number of ‘guarantees', such as, e.g., minimum accumulation rates, minimum annual payments and minimum total payout. Packaging different types of guarantees is the feature of the so-called Variable Annuities. Basically, these products are...

One of risk measures' key purposes is to consistently rank and distinguish between different risk profiles. From a practical perspective, a risk measure should also be robust, that is, insensitive to small perturbations in input assumptions. It is known in the literature Cont et al (2010),...

Major (2018) discusses Euler/Aumann-Shapley allocations for non-linear portfolios. He argues convincingly that many (re)insurance portfolios, while non-linear, are nevertheless positively homogeneous, owing to the way that deductibles and limits are typically set. For such non-linear but...

Sensitivity analysis is an important component of model building, interpretation and validation. A model comprises a vector of random input factors, an aggregation function mapping input factors to a random output, and a (baseline) probability measure. A risk measure, such as Value-at-Risk and...

The purpose of this paper is to conduct a market-consistent valuation of life insurance participating liabilities sold to a population of partially heterogeneous customers under the joint impact of biometric and financial risk. In particular, the heterogeneity between groups of policyholders...