Multivariate Stochastic Prioritization of Dependent Actuarial Risks Under Uncertainty

Abstract

The main prompting factor behind decision making is comparing or ordering risks. Risk management strategies should be based on the dynamics of stochastic ordering relations and influences of decision makers' tendencies on risk prioritization. The objective of this thesis is to construct a concept for stochastic risk prioritization of multivariate aggregate claims.

The definition of risk from perspectives of individuals, companies or governments may vary according to their risk perceptions, as risk is indicated not only by objective measures but also by subjective characteristics. In order to describe the risk accurately, the theoretical background of multivariate stochastic prioritization of dependent actuarial risks should be understood. For this aim, we familiarize ourselves with order theory that allows comparing and ordering objects characterized by multiple indicators.

Being an important issue of human behaviour, this area falls within the boundaries of several fields, one of which - public health - is our specific interest. We intend to apply the order theory to a chosen risk area such as foodborne or agricultural risks, since they are rather vulnerable aspects of public health. Analytic tools may not always be sufficient for prioritization especially when we work on environmental risks. Hence, geographic information system is a useful tool for risk prioritization in such cases.

In this thesis, we aim to prioritize aggregate claim vectors of different risk clusters in agricultural insurance under the assumption that the individual claims exposed to similar environmental risks are dependent. For this purpose, first we obtain risk clusters for a crop-hail insurance portfolio considering spatial and temporal features of hazard regions. We propose an extended approach for differential evolution optimization which determines the optimal sample set used in inverse distance weighting with reduction technique. Second, we prioritize the aggregate claims taken as actuarial risks by using various stochastic ordering relations that are studied within the framework of partial order theory. These relations are stochastic dominance, stochastic majorization and stop-loss dominance. Having discussed the concept of risk itself, we also investigate the risk measures which could be sufficient and accurate criteria for determining the riskiness of a portfolio.

The classical first-order stochastic dominance is useful to design the risk prioritization context. We also suggest stochastic majorization relation according to multivariate representation of actuarial risks. This relation is very beneficial for our study since it enables us to order aggregate claim vectors partially using Schur-convex risk measures.

On the other hand, we consider the impacts of risk perception on prioritization of risks. Working within this context and attempting to contribute to it, we seek for a behavioral approach which could enhance and facilitate the description of the choices individuals make in risky situations. An example of such approaches could be cumulative prospect theory (CPT), as a more accurate alternative to expected utility theory. In the stop-loss dominance context, we adapt the zero-utility premium principle in order to obtain solutions for stop-loss premiums and propose stop-loss dominance relation under CPT.