A variational inequality arising from optimal surrender of variable annuity with lookback benefit

We introduce a variable annuity (VA) contract with a surrender option and lookback benefit, that is, the benefit of the VA contract is linked to the maximum process of the policyholder’s account value. In contrast to the constant guarantee model provided in Bernard et al. (Insur. Math. Econ. 55:116–128, 2014), it is optimal for the policyholder of the VA contract with lookback benefit to surrender the VA contract when the policyholder’s account value is below or equal to the optimal surrender boundary. Thus, from the perspective of the insurer to construct a portfolio of VA contracts, utilizing the VA contracts with lookback benefit along with VA contracts with constant guarantee provides the diversification of early surrenders. The valuation of this contract can be described as a two-dimensional parabolic variational inequality. By converting this into the one-dimensional problem, we obtain the integral equations for the value function and the free boundary. The recursive integration method is applied to obtain the numerical solutions. We also provide comparative statics of the optimal surrender boundaries with respect to various parameters.

Adaptive Clinical Trial Designs with Surrogates: When Should We Bother?

The success of a new drug is assessed within a clinical trial using a primary endpoint, which is typically the true outcome of interest—for example, overall survival. However, regulators sometimes approve drugs using a surrogate outcome—an intermediate indicator that is faster or easier to measure than the true outcome of interest—for example, progression-free survival—as the primary endpoint when there is demonstrable medical need. Although using a surrogate outcome (instead of the true outcome) as the primary endpoint can substantially speed up clinical trials and lower costs, it can also result in poor drug-approval decisions because the surrogate is not a perfect predictor of the true outcome. In this paper, we propose combining data from both surrogate and true outcomes to improve decision making within a late-phase clinical trial. In contrast to broadly used clinical trial designs that rely on a single primary endpoint, we propose a Bayesian adaptive clinical trial design that simultaneously leverages both observed outcomes to inform trial decisions. We perform comparative statics on the relative benefit of our approach, illustrating the types of diseases and surrogates for which our proposed design is particularly advantageous. Finally, we illustrate our proposed design on metastatic breast cancer. We use a large-scale clinical trial database to construct a Bayesian prior and simulate our design on a subset of clinical trials. We estimate that our design would yield a 16% decrease in trial costs relative to existing clinical trial designs, while maintaining the same Type I/II error rates. This paper was accepted by J. George Shanthikumar for the Special Issue on Data-Driven Prescriptive Analytics.

Consumption Smoothing and Discounting in Infinite-Horizon, Discrete-Choice Problems

Suppose the consumption space is discrete. Our first contribution is a technical result showing that any continuous utility function of any stationary preference relation over infinite consumption streams has convex range, provided that the agent is sufficiently patient. Putting the result to use, we consider a model of endogenous discounting (a generalization of the standard model with geometric discounting) and show the uniqueness of the consumption-dependent discount factor as well as the cardinal uniqueness of utility. Comparative statics are then provided to substantiate the uniqueness. For instance, we show that, as in the more familiar case of an infinitely divisible good, the cardinal uniqueness of utility captures an agent’s desire to smooth consumption over time.

Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory

People take different measures to control risks. The measures that can simultaneously reduce loss probability and loss size are called self-insurance-cum-protection. This paper studies self-insurance-cum-protection using Yaari’s dual theory. We analyze the comparative statics of increased risk aversion. Two different sufficient conditions are found in the two-state model, from which an increase in the level of risk aversion will lead to an increase in the level of self-insurance-cum-protection. The first condition is a new result under Yaari’s dual theory and its implication is that the more risk-averse individual is willing to exert greater effort on self-insurance-cum-protection if the probability of loss can be reduced to very small by a less risk-averse individual with optimal effort. The second condition depends on the forms of the self-insurance-cum protection cost and the loss. This condition is the same as that obtained under expected utility in existing literature. Our study therefore assures the robustness this result. We also study comparative statics in the continuous model and find out that the results are analogous to that in the two-state model. In addition, we consider how the availability of market insurance affects the self-insurance-cum-protection level. When the probability of loss is small, the self-insurance-cum-protection and market insurance are substitutes. This means when market insurance is available, people tend to exert less effort on self-insurance-cum-protection.

Impact of the Digital Economy on the Priority Directions of Business Regulation

Aim. The presented study aims to determine the prerequisites and directions for the transformation of government regulation and support for business structures in the context of the digitalization of the economy and to propose approaches for assessing its implementation and specific tools that could help to solve problems of economic development.Tasks. The authors analyze government support for the business sector of the economy and identify its features at different stages of development; describe tools used for the management and support of business structures, identifying problems and opportunities for their successful application at the regional level to achieve sustainable economic growth in Russia.Methods. This study uses analysis and synthesis in comparative statics and in a dynamic context as well as historical, systems, and ex-ante approaches. Results. The study confirms that government regulation and support for entrepreneurship in the context of the digitalization of the economy should be considered within the framework of an integrated approach based on a dynamic analysis of indicators at the macro- and microlevel, which would make it possible to analyze the most vulnerable aspects of government support for business structures and to develop a roadmap of actions to be taken.Conclusions. The authors substantiate the necessity of using infrastructure tools in the management of entrepreneurial development in Russia to eliminate the constantly emerging and existing imbalances between the needs of digital development and lagging government influence. Adjustments that need to be made in monitoring, forecasting, planning, and control are identified. These adjustments would make it possible to implement the scenario approach to management, mitigating external and internal risks in the global market of goods and services.