An identity of hitting times and its application to the valuation of guaranteed minimum withdrawal benefit

In this paper we explore an identity in distribution of hitting times of a finite variation process (Yor's process) and a diffusion process (geometric Brownian motion with affine drift), which arise from various applications in financial mathematics. As a result, we provide analytical solutions to the fair charge of variable annuity guaranteed minimum withdrawal benefit (GMWB) from a policyholder's point of view, which was only previously obtained in the literature by numerical methods. We also use complex inversion methods to derive analytical solutions to the fair charge of the GMWB from an insurer's point of view, which is used in the market practice, however, based on Monte Carlo simulations. Despite of their seemingly different formulations, we can prove under certain assumptions the two pricing approaches are equivalent.Comment: 25 pages, 2 figure

Cyber Risk Assessment for Capital Management

Cyber risk is an omnipresent risk in the increasingly digitized world that is known to be difficult to manage. This paper proposes a two-pillar cyber risk management framework to address such difficulty. The first pillar, cyber risk assessment, blends the frequency-severity model in insurance with the cascade model in cybersecurity, to capture the unique feature of cyber risk. The second pillar, cyber capital management, provides informative decision-making on a balanced cyber risk management strategy, which includes cybersecurity investments, insurance coverage, and reserves. This framework is demonstrated by a case study based on a historical cyber incident dataset, which shows that a comprehensive cost-benefit analysis is necessary for a budget-constrained company with competing objectives for cyber risk management. Sensitivity analysis also illustrates that the best strategy depends on various factors, such as the amount of cybersecurity investments and the effectiveness of cybersecurity controls.Comment: This paper was first presented on July 5, 2021, at the 24th International Congress on Insurance: Mathematics and Economic

Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model

This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk models in the literature. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme, by solving the associated integro-differential quasi-variational inequality, we obtain the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates.Comment: Key Words: Piecewise-deterministic compound Poisson model, optimal stochastic control, HJB equation, quasi-variational inequality, threshold strategy, barrier strateg

Decentralized Insurance: Technical Foundation of Business Models

Buku ini membahas tentang fondasi teknis model bisnis terbaru perusahaan asuransi. Ini memberikan suatu pendekatan inovatif yang diharapkan dapat membantu memitigasi konflik yang melekat pada asuransi komersial untuk mengurangi perilaku curang, dan untuk memberikan harga yang lebih rendah. Hal ini juga dapat membantu menjadikan asuransi lebih transparan dan eksplisit. Untuk model bisnis terbaru ini bergantung pada inovasi teknologi seperti Keuangan Terdesentralisasi.xxiii, 263 p

An operator-based approach to the analysis of ruin-related quantities in jump diffusion risk models

Recent developments in ruin theory have seen the growing popularity of jump diffusion processes in modeling an insurer's assets and liabilities. Despite the variations of technique, the analysis of ruin-related quantities mostly relies on solutions to certain differential equations. In this paper, we propose in the context of Lévy-type jump diffusion risk models a solution method to a general class of ruin-related quantities. Then we present a novel operator-based approach to solving a particular type of integro-differential equations. Explicit expressions for resolvent densities for jump diffusion processes killed on exit below zero are obtained as by-products of this work.Jump diffusion process Ruin theory Expected discounted penalty at ruin Integro-differential equation Operator calculus Resolvent density