Tail Fitting Probability Distributions for Risk Management Purposes

The same processors that once fueled the Bitcoin gold rush and now train cutting-edge AI like ChatGPT are quietly revolutionizing actuarial science. While cryptocurrencies harnessed GPU power to mine digital coins, and AI uses it to process billions of data points, actuaries are discovering these chips can run complex mortality simulations in minutes instead of days. What began as hardware for gaming graphics has become our most powerful tool - turning overnight batch processes into real-time analytics and making trillion-scenario modeling suddenly practical. This presentation will explore how this transformative technology is reshaping our field, and why the actuaries who master GPU computing will lead the next wave of insurance innovation.

This paper is an extension of the “Insurance Risk with Markov Chain Monte Carlo (MCMC) and Method of Moments (MM)”, the method is applied to a portfolio of insurance policies with guaranteed profitability and surrender option. Retrospective valuation is associated with the debt that is reported to the policyholder by the insurer. On the other hand, the insurer performs the prospective valuation of the cash flow that must be discounted with a yield curve, and which must contain the surrender option by the insured. For discrete-time stochastic scenarios, it is feasible to determine the structure of the probability distribution of future flows, which is not necessarily a normal distribution. It will be demonstrated by MM that for insurance with a surrender option, such as endowment or whole life, the expectation of future flows E(BEL) and its respective future variance V(BEL), can be obtained, both in present value, and as a consequence, calculate the contractual insurance margin (MCS) of the insurer. It will also be shown that by MCMC the convergence of the mean (BEL) and sample variance σ^2 (BEL), the probability distribution of future (MCS) flows will be graphed in 2 and 3 dimensions as a function of time. Likewise, it will be demonstrated that there is no single scalar statistic that, when multiplied by the σ(BEL) standard deviation, results in a standardized risk adjustment.

This research discusses the design, implementation, and performance of AI agents to meet regulatory standards and industry requirements. AI-enhanced ALM can better manage risks and optimize portfolio performance under various market conditions compared to traditional methods. The integration of AI in ALM processes presents promising opportunities for actuaries to advance their risk management frameworks, providing enhanced value to stakeholders in volatile economic landscapes.

Advanced solvency frameworks, such as Solvency II, require both a regulatory balance sheet separate from a statutory one and a standardized solvency capital model, imposing high demands that are very challenging in both setup and oversight for regulators and operators in non-mature insurance markets. This paper proposes a simplified risk-based capital scheme based on the Premium Allocation Approach (PAA) under IFRS 17, aligned with the International Association of Insurance Supervisors (IAIS) Insurance Core Principles (ICPs), to provide an accessible and practical solvency framework tailored for such markets. This approach streamlines capital calculations, minimizes data demands, and simplifies compliance processes, making it feasible for insurers and regulators in developing countries to adopt a risk-based regime without the extensive rigor of mature frameworks. As a simpler alternative, the framework is flexible enough to accommodate additional accounting standards, such as GAAPs, making it suitable for a range of regulatory environments. The framework facilitates faster implementation of risk-based regulatory systems, supporting financial stability and growth within different insurance markets. It offers a balanced solution that maintains alignment with key principles of capital adequacy and solvency, while addressing the specific constraints faced by developing nations or small insurers.