This paper investigates an optimal reinsurance policy using a risk model with dependent claim and insurance premium by assuming that the insurance premium is random. Their dependence structure is modeled using Sarmanov’s bivariate exponential distribution and the Farlie–Gumbel–Morgenstern...

To manage market and longevity risk, Dr. Pfau shows how the use of life insurance and income annuities, as fixed income assets in a portfolio, can better hedge a retiree’s retirement-income needs as a portfolio volatility reduction tool

We develop a theory that connects insurance premiums, insurance companies’ investment behavior, and equilibrium asset prices. Consistent with the model's key predictions, we show empirically that (1) insurers with more stable insurance funding take more investment risk and, therefore, earn...

This tutorial gives an overview of SHAP (SHapley Additive exPlanation), one of the most commonly used techniques for examining a black-box machine learning (ML) model. Besides providing the necessary game theoretic background, we show how typical SHAP analyses are performed and used to gain...

The study of actuarial fairness in auto insurance has been an important issue in the decision making of rate regulation. Risk classification and estimating risk relativities through statistical modeling become essential to help achieve fairness in premium rates. However, because of minor...

We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing discounted dividends until simultaneous ruin of both branches of...

In this paper, we present extensions of the Hatzopoulos-Sagianou (2020) (HS) multiple-component stochastic mortality model. Our aim is to thoroughly evaluate and stress test the HS model by deploying various link functions, using generalised linear models, and diverse distributions in the...

For annuity providers, a higher life expectancy is not always positive news, as it potentially implies increased future costs, since benefits must be provided over a longer period of time. The underlying risk behind the unexpected improvement in life expectancy is called longevity risk. One way...

Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their risk to a reinsurance company. Ruin probabilities allow us to measure the effect of stop-loss reinsurance on the solvency of the primary insurer. They further permit the calculation of the...

The Guaranteed Minimum Maturity Benefit is quite a popular feature embedded in several unit-linked policies offered by insurance companies. The value of this benefit depends on several processes assumed to describe both the mortality and the financial dynamics, typically represented by interest...

Actuarial fairness pertains to the situation in which the price of an insurance contract is equal to its expected outcome. This paradigm is at odds with financial pricing: If two financial contracts have the same expected value, but one is better than the other in the sense of second order...

The aim of these Lecture Notes is to complement the material, concerning Life Insurance, presented in the textbook by A. Olivieri and E. Pitacco, “Introduction to Insurance Mathematics. Technical and Financial Features of Risk Tansfers”, by providing the basics of a time-continuous setting...

In this paper we consider a discrete-time risk model, which allows the premium to be adjusted according to claims experience. This model is inspired by the well-known bonus-malus system in the non-life insurance industry. Two strategies of adjusting periodic premiums are considered: aggregate...

The valuation of insurance liabilities has traditionally been dealt with by actuaries, who closely monitored underlying illiquid features, assumed a long-term perspective, and exercised their own subjective, expert judgment. However, the new EU regulatory regime of Solvency II (S2) has come to...

A funded social security retirement program would imply a larger capital stock and a higher level of real income than an unfunded program that provides the same level of benefits. The transition from an unfunded program to a funded program that does not reduce the benefits of existing retirees...

In this paper we address the question of how the generosity of the benefit rule of the German public pension system has changed during the past three decades and how this development can be explained by demographic changes. Firstly, we illustrate the political risk of benefit rule changes for...

This paper introduces a new R package, LRMoE, a statistical software tailor-made for actuarial applications which allows actuarial researchers and practitioners to model and analyze insurance loss frequencies and severities using the Logit-weighted Reduced Mixture-of-Experts (LRMoE) model. LRMoE...

The objective of this paper is twofold. On the one hand, the optimal combination of reinsurance and financial investment is studied under a general framework, since there is no specific type of reinsurance contract, there is no specific dynamics of the financial instruments, the financial market...

The traditional approach to flexible retirement (e.g. NDC) neglects the impact of asymmetric information on actuarial fairness (neutrality). The mechanism design approach (e.g. Diamond, 2003) gives up the requirement of neutrality and looks for a redistributive second-best benefit-retirement-age...

Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematically-inclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious...

In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and...

While abundant empirical studies support the long-range dependence (LRD) of mortality rates, the corresponding impact on mortality securities are largely unknown due to the lack of appropriate tractable models for valuation and risk management purposes. We propose a novel class of Volterra...

Financial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product's payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically...

In this paper, we investigate the fair valuation of insurance liabilities in a dynamic multi-period setting. We define a fair dynamic valuation as a valuation which is actuarial (mark-to-model for claims independent of financial market evolutions), market-consistent (mark-to-market for any...

A simple formula for non-discriminatory insurance pricing is introduced. This formula is based on the assumption that certain individual (discriminatory) policyholder information is not allowed to be used for insurance pricing. The suggested procedure can be summarized as follows: First, we...

Very similar modeling is done for actuarial models in loss reserving and mortality projection. Both start with incomplete data rectangles, traditionally called triangles, and model by year of origin, year of observation, and lag from origin to observation. Actuaries using these models almost...

The insurance industry is built on risk classification, grouping insureds into homogeneous classes. Through actions such as underwriting, pricing and so forth, it differentiates, or discriminates, among insureds. Actuaries have responsibility for pricing insurance risk transfers and are...

"In order to make insurance a trade at all, the common premium must be sufficient to compensate the common losses, to pay the expense of management, and to afford such a profit as might have been drawn from an equal capital employed in any common trade. Pricing insurance risk is the last mile of...

Risk measures in finance and insurance -- Fixed-probability level in a diffusion model -- Fixed-probability level in an exceptional renewal model -- Implicit function defined by M-equation -- Fixed-probability level in general renewal model -- Case study : numerical evaluation of...

"This book provides a thorough understanding of the fundamental concepts of financial mathematics essential for the evaluation of any financial product and instrument. Mastering concepts of present and future values of streams of cash flows under different interest rate environments is core for...