Book Description

In non-life insurance, a loss reserve represents the insurer's best estimate of outstanding liabilities for losses that occurred on or before a valuation date. The accurate prediction of outstanding liabilities is key to setting reserves and calibrating insurance rates, which are two interconnected primary functions of actuaries. For instance, inadequate reserves could lead to deficient rates and thereby increase solvency risk. Also, excessive reserves could increase the cost of capital and regulatory scrutiny. Therefore, reserving accuracy is essential for insurers to meet regulatory requirements, remain solvent, and stay competitive. The loss reserve prediction in non-life insurance is usually based on macro-level models that use aggregate loss data summarized in a run-off triangle. The main strengths of the macro-level models are that they are easy to implement and interpret. But, the limited ability to handle heterogeneity among triangle cells and changes to the business environment may lead to inaccurate predictions. Recently, micro-level reserving techniques have gained traction as they allow an analyst to use the information on the policy, the individual claim, and the development process to predict outstanding liabilities. Granular covariate information allows environmental changes to be captured naturally to improve reserve predictions. In non-life insurance, the payment history can be predictive of the timing of a settlement for individual claims. Ignoring the association between the payment process and the settlement process could bias the prediction of outstanding payments. To address this issue, In this dissertation, I introduce into the literature of micro-level loss reserving a joint modeling framework that incorporates longitudinal payments of a claim into the intensity process of the claim settlement. I discuss statistical inference and focus on the prediction aspects of the model. I demonstrate applications of the proposed model in the reserving practice and identify scenarios where the joint model outperforms macro-level reserving methods using simulated data. Moreover, I present a detailed empirical analysis using data from a property insurance provider. I fit the joint model to a training dataset and use the fitted model to predict the future development of open claims. The prediction results using out-of-sample data show that the joint model framework outperforms existing reserving models that ignore the payment-settlement association. In pricing insurance contracts for non-life insurers, current methods often only consider the information on closed claims and ignore open claims. In case of a shift in the insurer's book risk profile, open claims could reflect the change in a timely manner compared to closed claims. This dissertation presents an intuitive ratemaking model by employing a marked Poisson process framework. The framework ensures that the multivariate risk analysis is done using the information on all reported claims and makes an adjustment for incurred but not reported claims based on the reporting delay distribution. Using data from a property insurance provider, I show that by determining rates based on current data, the proposed ratemaking framework leads to better alignment of premiums with claims experience. Among other things, accurate risk pricing suggests that all market participants, insurers, and customers, bear reasonable costs for risks assumed.