Abstract: In this paper we introduce a new coherent cumulative risk measure on a subclass in the space of càdlàg processes. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. We focus our motivation and discussion on the problem of capital allocation. Indeed, this risk measure is well-suited to address the problem of capital allocation in an insurance context. We show that the capital allocation problem for this risk measure has a unique solution determined by the Euler allocation method. Some examples and connections with existing results as well as practical implications are also discussed.
Abstract: In problems of optimal insurance design, Arrow’s classical result on the optimality of the deductible indemnity schedule holds in a situation where the insurer is a risk-neutral Expected-Utility (EU) maximizer, the insured is a risk-averse EU-maximizer, and the two parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. Recently, Ghossoub re-examined Arrow’s problem in a setting where the two parties have different subjective beliefs about the realizations of the insurable random loss, and he showed that if these beliefs satisfy a certain compatibility condition that is weaker than the Monotone Likelihood Ratio (MLR) condition, then optimal indemnity schedules exist and are nondecreasing in the loss. However, Ghossoub only gave a characterization of these optimal indemnity schedules in the special case of an MLR. In this paper, we consider the general case, allowing for disagreement about zero-probability events. We fully characterize the class of all optimal indemnity schedules that are nondecreasing in the loss, in terms of their distribution under the insured’s probability measure, and we obtain Arrow’s classical result, as well as one of the results of Ghossoub as corollaries. Finally, we formalize Marshall’s argument that, in a setting of belief heterogeneity, an optimal indemnity schedule may take “any”shape.
Abstract: Extreme weather and climate change can have a significant impact on all types of infrastructure and assets, regardless of location, with the potential for human casualties, physical damage to assets, disruption of operations, economic and community distress, and environmental degradation. This paper describes a methodology for using extreme weather and climate data to identify climate-related risks and to quantify the potential impact of extreme weather events on certain types of transportation infrastructure as part of a vulnerability screening assessment. This screening assessment can be especially useful when a large number of assets or large geographical areas are being studied, with the results enabling planners and asset managers to undertake a more detailed assessment of vulnerability on a more targeted number of assets or locations. The methodology combines climate, weather, and impact data to identify vulnerabilities to a range of weather and climate related risks over a multi-decadal planning period. The paper applies the methodology to perform an extreme weather and climate change vulnerability screening assessment on transportation infrastructure assets for the State of Tennessee. This paper represents the results of one of the first efforts at spatial vulnerability assessments of transportation infrastructure and provides important insights for any organization considering the impact of climate and weather events on transportation or other critical infrastructure systems.
Abstract: The aim of this paper is to understand and to model claims arrival and reporting delay in general insurance. We calibrate two real individual claims data sets to the statistical model of Jewell and Norberg. One data set considers property insurance and the other one casualty insurance. For our analysis we slightly relax the model assumptions of Jewell allowing for non-stationarity so that the model is able to cope with trends and with seasonal patterns. The performance of our individual claims data prediction is compared to the prediction based on aggregate data using the Poisson chain-ladder method.
Abstract: We study risk-minimization for a large class of insurance contracts. Given that the individual progress in time of visiting an insurance policy’s states follows an -doubly stochastic Markov chain, we describe different state-dependent types of insurance benefits. These cover single payments at maturity, annuity-type payments and payments at the time of a transition. Based on the intensity of the -doubly stochastic Markov chain, we provide the Galtchouk-Kunita-Watanabe decomposition for a general insurance contract and specify risk-minimizing strategies in a Brownian financial market setting. The results are further illustrated explicitly within an affine structure for the intensity.
Abstract: This paper studies the problem of optimal reinsurance contract design. We let the insurer use dual utility, and the premium is an extended Wang’s premium principle. The novel contribution is that we allow for heterogeneity in the beliefs regarding the underlying probability distribution. We characterize layer-reinsurance as an optimal reinsurance contract. Moreover, we characterize layer-reinsurance as optimal contracts when the insurer faces costs of holding regulatory capital. We illustrate this in cases where both firms use the Value-at-Risk or the conditional Value-at-Risk.