This paper provides a model for allocating capital to different insurance lines with varying development periods for a value-maximizing insurance company. In our model, the company makes capitalization and exposure decisions considering its capital level and its relevant loss history. As in simpler settings, the optimal portfolio can be characterized via risk-adjusted return ratios, although the model attaches different valuation weights to cash flows with different tenors. Numerical results show that our approach yields substantively different guidance relative to that obtained from conventional capital allocation approaches, particularly on the relative valuation of long-tailed versus short-tailed liabilities, since long-tailed lines can provide a source of short-term financing. We discuss robustness and implications of our findings.

We extend the conventional life-cycle framework for valuing health and longevity improvements to a stochastic setting with multiple health states and apply it to data on mortality, quality of life, labor earnings, and medical spending for adults with different comorbidities. We find that sick adults are willing to pay nearly twice as much per quality-adjusted life-year (QALY) to reduce mortality risk as healthy adults, and that reducing the risk of serious illness is valued similarly to reducing the risk of mild illness. Our results provide a rational explanation for why people oppose a single threshold value for rationing care and why they invest less in prevention than in treatment.

With increasing data availability, the use of machine learning methods has gained popularity in insurance. Applications include novel areas for the use of models, for instance for automating business processes, as well as conventional actuarial prediction tasks such as claims or loss prediction. However, with the limited amount of labeled data due to claims being a rare occurrence, the superiority of advanced learners-particularly deep neural networks that have led to major advances in other domains-remains unclear. In other fields, transfer learning has been proposed as a potential solution in similar contexts. Transfer learning refers to taking the knowledge from one problem and applying it to a new but related problem, which can reduce the cost of collecting additional labeled data and improve the model performance. In this article, various transfer learning approaches are introduced and applied to publicly available insurance data sets. The performance of each approach is evaluated compared to a baseline model in the context of predicting insurance claims. The results highlight transfer learning as a useful tool for the actuarial toolkit.

Variable Annuities, which comprise a substantial proportion of the retirement products sold by insurance companies, have become increasingly complex over the past decades. We investigate the drivers of the product trends. We distinguish "virtuous" innovations that expand upon the existing set of consumption paths in retirement from "obfuscating" innovations that increase complexity without clear benefits to consumers. We document a recurring pattern where, in each benefit category, obfuscating products follow the introduction of virtuous innovations. This pattern generates the overall increase in product complexity. Our results challenge prevailing perspectives on Variable Annuities in the popular press and the literature.

This article comments on the paper "Less-expensive long-term annuities linked to mortality, cash and equity" by Kevin Fergusson and Eckard Platen, appearing in this issue of the Annals of Actuarial Science. It adds two perspectives to their thought-provoking contribution. The first is a similarity to some recent work in quantitative finance on "deep hedging" that leverages machine learning models to find the cheapest replication strategy for a derivative payoff in a largely model-free setting. The second perspective engages with some of the interesting implications of their approach and draws parallels to literature in asset pricing and macro-finance. These perspectives point to the potential need for more fundamental shifts than the authors of the paper are advertising.

Capturing the Uncertainty in Long-Term Mortality Forecasts The uncertainty in future longevity presents a substantial risk factor for insurance companies, pension funds, and retirement systems. In “Modeling the Risk in Mortality Projections,” Zhu and Bauer present novel stochastic models for analyzing this longevity risk that focus on the uncertainty associated with long-term mortality projections and capture the evolution of mortality forecasts over the past decades. They arrive at their models by analyzing time series of mortality forecasts in a forward modeling framework, which contrasts with conventional stochastic mortality models that are built on age-specific realized mortality rates. The authors showcase their models in exemplifying financial applications in both traditional life insurance markets and the emerging longevity risk transfer market. A key takeaway is that uncertainty in positions that depend on the long-term evolution of mortality is substantially greater under their models than suggested by conventional models.

The estimation of enterprise risk for financial institutions entails a re-evaluation of the company's economic balance sheet at a future time for a (large) number of stochastic scenarios. The current paper discusses tackling this nested valuation problem based on least-squares Monte Carlo techniques familiar from American option pricing. We formalise the algorithm in an operator setting and discuss the choice of the regressors ("basis functions"). In particular, we show that the left singular functions of the corresponding conditional expectation operator present robust basis functions. Our numerical examples demonstrate that the algorithm can produce accurate results at relatively low computational costs.

Typical Variable Annuity products combine complex baseline contracts at considerable fees with optional guarantees. We argue this product design is driven by benefits of bundling to the provider, to the extent that the baseline option features can reduce total replication value. This is possible due to market frictions, and particularly taxation rules, affecting policyholder exercise behavior. We demonstrate the relevance of this mechanism in the context of popular withdrawal guarantees, both theoretically and empirically. Specifically, we show that in the presence of personal taxes, adding on a common death benefit at baseline decreases the total contract value to the provider.

Capital allocation is an essential task for risk pricing and performance measurement of insurance business lines. This paper provides a survey of existing capital allocation methods, including common approaches based on the gradients of risk measures and economic allocation arising from counterparty risk aversion. We implement all methods in two example settings: binomial losses and loss realizations from a catastrophe reinsurer. We assess stability based on sensitivity analysis with regard to losses. Our results show that capital allocations appear to be intrinsically (geometrically) related, although the stability varies considerably. We find stark differences between common and “economic” capital allocations. This paper was funded through Casualty Actuarial Society sponsored research on “Allocation of Costs of Holding Capital”. Address for Correspondence: qguo@bsu.edu

We revisit the foundations of economic capital and RAROC calculations prevalent in the insurance industry by extending the canonical static setting to a dynamic model with different ways of raising capital. The dynamic results suggest two important modifications to the conventional approach to risk measurement and capital allocation. First, "capital" should be defined broadly to include the continuation value of the firm. Second, cash flow valuations must reflect risk adjustments to account for company effective risk aversion. We illustrate these results in a calibrated version of our model using data from a catastrophe reinsurer. We find that the dynamic modifications are practically significant—although static approximations with a properly calibrated company risk aversion are quite accurate.

Journal of Risk and InsuranceVolume 88, Issue 3 p. 525-528 SYMPOSIUM ON INSURE-TECH, DIGITALIZATION, AND BIG-DATA TECHNIQUES IN RISK MANAGEMENT AND INSURANCE Symposium on insure-tech, digitalization, and big-data techniques in risk management and insurance Daniel Bauer, Corresponding Author Daniel Bauer daniel.bauer@wisc.edu Department of Risk and Insurance, University of Wisconsin-Madison, Madison, Wisconsin, USA CorrespondenceDaniel Bauer, Department of Risk and Insurance, University of Wisconsin-Madison, 975 University Ave, Madison, WI 53706, USA. Email: daniel.bauer@wisc.eduSearch for more papers by this authorJames Tyler Leverty, James Tyler Leverty Department of Risk and Insurance, University of Wisconsin-Madison, Madison, Wisconsin, USASearch for more papers by this authorJoan Schmit, Joan Schmit Department of Risk and Insurance, University of Wisconsin-Madison, Madison, Wisconsin, USASearch for more papers by this authorJustin Sydnor, Justin Sydnor Department of Risk and Insurance, University of Wisconsin-Madison, Madison, Wisconsin, USASearch for more papers by this author Daniel Bauer, Corresponding Author Daniel Bauer daniel.bauer@wisc.edu Department of Risk and Insurance, University of Wisconsin-Madison, Madison, Wisconsin, USA CorrespondenceDaniel Bauer, Department of Risk and Insurance, University of Wisconsin-Madison, 975 University Ave, Madison, WI 53706, USA. Email: daniel.bauer@wisc.eduSearch for more papers by this authorJames Tyler Leverty, James Tyler Leverty Department of Risk and Insurance, University of Wisconsin-Madison, Madison, Wisconsin, USASearch for more papers by this authorJoan Schmit, Joan Schmit Department of Risk and Insurance, University of Wisconsin-Madison, Madison, Wisconsin, USASearch for more papers by this authorJustin Sydnor, Justin Sydnor Department of Risk and Insurance, University of Wisconsin-Madison, Madison, Wisconsin, USASearch for more papers by this author First published: 29 July 2021 https://doi.org/10.1111/jori.12360 We thank Vallabh (Samba) Sambamurthy for helpful perspectives and members of American Family Insurance for their input on specific questions of digitalization. Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume88, Issue3September 2021Pages 525-528 RelatedInformation

We reexamine life insurance and annuity pricing during the 2008 financial crisis. In contrast with previous research, we find that insurers sold policies at significantly elevated markups over their fundamental values during the crisis months and, moreover, that statutory accounting pressures had the effect of increasing rather than decreasing prices. We show that the experience in 2008 was not extraordinary but instead mirrored earlier episodes where corporate borrowing rates rose quickly, such as 1994 and 1999.

To infer forward-looking, market-based mortality trends, we estimate a flexible affine stochastic mortality model based on a set of U.S. term life insurance prices using a generalized method of moments approach. We find that neither mortality shocks nor stochasticity in the aggregate trend seem to affect the prices. In contrast, allowing for heterogeneity in the mortality rates across carriers is crucial. We conclude that for life insurance, rather than aggregate mortality risk, the key risks emanate from the composition of the portfolio of policyholders. These findings have consequences for mortality risk management and emphasize important directions for mortality-related actuarial research.

The decomposition of dynamic risks a company faces into components associated with various sources of risk, such as financial risks, aggregate economic risks, or industry-specific risk drivers, is of significant relevance in view of risk management and product design, particularly in (life) insurance. Nevertheless, although several decomposition approaches have been proposed, no systematic analysis is available. This paper closes this gap in literature by introducing properties for meaningful risk decompositions and demonstrating that proposed approaches violate at least one of these properties. As an alternative, we propose a novel martingale representation theorem ( MRT ) decomposition that relies on martingale representation and show that it satisfies all of the properties. We discuss its calculation and present detailed examples illustrating its applicability. This paper was accepted by Baris Ata, stochastic models and simulation .

We use data from a large US life expectancy provider to test for asymmetric information in the secondary life insurance—or life settlements—market. We compare realized lifetimes for a subsample of settled policies relative to all (settled and nonsettled) policies, and find a positive settlement‐survival correlation indicating the existence of informational asymmetry between policyholders and investors. Estimates of the “excess hazard” associated with settling show the effect is temporary and wears off over approximately 8 years. This indicates individuals in our sample possess private information with regards to their near‐term survival prospects and make use of it, which has economic consequences for this market and beyond.

Capital allocation models generally assume that the risk portfolio is constructed at a single point in time, when the underwriter has full information about available underwriting opportunities. However, in practice, opportunities are not all known at the beginning but instead arrive over time. Moreover, a commitment to an opportunity is not easy to change as time passes. Thus, to optimize a portfolio, the underwriter must make decisions on opportunities as they arrive while making use of assumptions about what will arrive in the future. This paper studies capital allocation rules in this setting, finding important differences from the static setting. The pricing of an opportunity is based on an expected future marginal cost of risk associated with that opportunity—one that will be fully understood only after the risk portfolio is finalized. The risk charge for today's opportunity is thus a probability-weighted average of the product of the marginal value of capital in future states of the world and the amount of capital consumed by the opportunity in those future states. Our numerical examples illustrate how the marginal cost of risk for an opportunity is shaped by when it arrives in time, as well as what has arrived before it.

Zielsetzung: Das seit uber 30 Jahren etablierte, individualisierte zweistufige Auswahlverfahren Humanmedizin der Universitat Witten/Herdecke (UW/H) umfasst explizite und implizite Auswahlkriterien. Zielsetzung dieser Analyse sind die Identifikation der impliziten Kriterien und die Beantwortung der Fragestellung, ob eine interne Konsistenz dieser impliziten Kriterien in den verschiedenen Phasen des Auswahlverfahrens (bei der Bewertung der Motivationsschreiben, wahrend des Auswahlwochenendes und bei den Abschlussgesprachen der Gutachtenden) belegt werden kann. Methodik: Drei qualitative Untersuchungen zu allen Phasen des Auswahlverfahrens an der UW/H wurden zur Ermittlung der impliziten Bewertungskriterien der Gutachtenden durchgefuhrt: 1. Motivationsschreiben im Extremgruppenvergleich (12 Zusagen versus 18 Absagen); 2. teilstrukturierte Experteninterviews (N=25) zum Auswahlwochenende; 3. Fokusgruppenanalyse zur Abschlussdiskussion an zwei Auswahlwochenenden (N=16). Ergebnisse: Inhaltsanalytisch ergaben sich bei den Motivationsschreiben 14 Hauptkategorien mit deutlichen Unterschieden zwischen den Extremgruppen in den Kategorien Schullaufbahn, Bewerbungsgrunde und Reflexionen sowie in der Abiturnote. Aus den Experteninterviews wurden die drei Hauptkategorien intellektuelle Fahigkeiten, Motivation und soziale Kompetenzen identifiziert sowie die Reflexionsfahigkeit als inhaltlich ubergreifende Kategorie. Die Fokusgruppenanalyse ergab die vier Hauptkategorien Leistung, Personlichkeit, Entwicklungsfahigkeit und Reflexionsfahigkeit. Die Reflexionsfahigkeit wurde dabei am haufigsten als Bewertungskriterium genannt. Schlussfolgerung: Hauptkategorien der Bewertung sind die Motivation fur den Arztberuf und das Studium an der UW/H; Leistung und Studierfahigkeit; Personlichkeit, Entwicklungsfahigkeit und soziale Kompetenz sowie Reflexionsfahigkeit als wichtigste zugrunde liegende Kompetenz und ubergreifende Kategorie. Die Reflexionsfahigkeit gilt dabei aus Sicht der Gutachterinnen und Gutachter als Pradiktor fur eine lebenslange professionelle Entwicklung als Arztin oder Arzt.

We develop and apply a generalized framework for valuing health and longevity improvements that departs from conventional assumptions of full annuitization and deterministic mortality. In contrast to conventional theory, we find a given mortality improvement may be worth more, not less, to patients facing shorter lives. Using real-world data, we calculate that severe illness can increase the value of statistical life by over $1 million. This result reconciles an anomaly in the research on preferences for life-extension. Moreover, our framework can value the prevention of mortality and of illness. We calculate that treating illness is up to an order of magnitude more valuable to consumers than prevention, even when both extend life equally. This asymmetry helps explain low observed investment in preventive care. Finally, we show that retirement annuities boost aggregate demand for life-extension. For instance, Social Security adds $11.5 trillion (10.5 percent) to the value of post-1940 longevity gains.