PhD Defense Oliver Lunding Sandqvist
Title: Stochastic modeling, sampling effects, and efficient estimation with applications to disability insurance
Abstract:
This thesis consists of a series of independent investigations related to multistate modeling, unified by their relevance to actuarial modeling of disability insurance policies. Chapter 1 sets the stage for the investigations in the subsequent chapters and provides an overview of the thesis’s main contributions.
Chapter 2 complements the introduction, describing practical challenges and opportunities for modeling and risk management of disability insurance portfolios. It is highlighted that the presence of public benefits, claim settlement processes, and prevention initiatives increases the complexity of the insurance business substantially and that these aspects have received limited attention in the literature. Subsequently, potential approaches and avenues for future research are outlined.
Chapters 3 and 4 are concerned with adapting multistate reserving models to situations where the payments and information might not be fully up to date. In Chapter 3, we consider a general formulation where the payments in real-time arise as running payments based on the available information and backpay based on the arrival of new information. In this setting, it is possible to link the present value to the classic present value based on the contractual payments and to characterize the dynamics of the reserve. However, it is in general not possible to link the reserve to the classic multistate reserve, and this hence has to be investigated in concrete models. Chapter 4 proposes a model for disability insurance schemes and imposes relevant conditional independence assumptions in order to obtain explicit expressions for the reserves as natural modifications of the classic multistate reserves. The potential financial impact is illustrated by applying the methods to a novel dataset LEC-DK19 which is based on real data that has been anonymized and slightly altered. The estimation procedure developed in Chapter 5 is used to operationalize the model.
In Chapter 5, the focus is on estimation of multistate models affected by various forms of missingness including reporting delays and incomplete event adjudication. An estimation procedure is proposed, accommodating reporting delays by thinning and incomplete adjudication by imputation, making effective use of the available data. The large sample properties of the estimator are established based on M-estimation theory. We demonstrate the approach on simulated data and on LEC-DK19.
The final chapter, Chapter 6, considers efficient and robust statistical inference in the presence of right-censoring. A flexible nonparametric estimation procedure based on pseudo-values and cross-fitting is proposed, allowing one to leverage prediction methods from machine learning. Large sample properties of the procedure are established, showing that the approach is doubly robust with respect to those nuisance parameters that are needed to compute the pseudo-values. A simulation study investigates the performance of the approach. Finally, we apply the estimation procedure to conduct a regression discontinuity design using real data.
Supervisors:
Associate Professor Christian Furrer, University of Copenhagen
PhD Lars Frederik Brandt, PFA Pension
Professor Mogens Steffensen, University of Copenhagen
Affiliated Professor Kristian Buchardt, AP Pension & University of Copenhagen
PhD Niklas Lindholm, PFA Pension
Assessment committee:
Professor Mogens Bladt (chairperson), University of Copenhagen, Denmark
Professor Marcus Christiansen, Carl von Ossietzky, Universität Oldenburg, Germany
Professor Katrien Antonio, KU Leuven, Belgium