Variable annuity guaranteed lifetime withdrawal benefit and decentralized insurance

Abstract

In this thesis, we mainly consider two aspects related to variable annuity guaranteed lifetime withdrawal benefit and peer-to-peer risk sharing. In the first part of this thesis, we study the variable annuity with guaranteed benefits. We model the guaranteed lifetime withdrawal benefit (GLWB) with step-up and roll-up features, and provide unique formulations of the valuation problem under various fee structures applying local time in stochastic analysis. Consequently, the work presents semi-analytical solutions for the risk-neutral value of GLWB riders. The principal-agent problem for variable annuities is also studied in the context of variable annuity guaranteed benefits and various fee incentives structures are compared.

In the second part, we present various new forms of decentralized insurance and develop a quantitative framework in which they are placed on a spectrum of decentralization. As a result, optimal risk pooling strategies are analyzed in an effort to understand participants' rational economic behaviors. Besides, a novel peer-to-peer risk-sharing framework is proposed and it aims to devise a risk allocation mechanism that is structurally decentralized, Pareto optimal, and mathematically fair. An explicit form for the pool allocation ratio matrix is derived, and convex programming techniques are applied to determine the optimal pooling mechanism in a constrained variance reduction setting. A tiered hierarchical generalization is also constructed to improve computational efficiency.