Some people have optimistic expectations regarding their accident probability, and thus, refrain from purchasing adequate insurance. This study investigates how insurance firms use advertisements to lower the ratio of optimistic individuals in the market. The main results are as follows: first, the optimal level of advertisements is maximized when the insurance premium is moderate. Second, the maximum level of advertisement varies according to the degree of optimism, which is measured by the difference between accurate and optimistic accident probabilities. Third, the advertisement decision is affected by the free-rider problem, and the equilibrium number of insurance firms with advertisement is always larger than that of firms without advertisement in a competitive insurance market.
For observations over a period of time, Bayesian credibility premium may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate Bayesian credibility premium under a change of probability measure within the copula framework. Such reformulation is demonstrated using the multivariate generalized beta of the second kind (GB2) distribution. Within this family of GB2 copulas, we are able to derive explicit form of Bayesian credibility premium. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case.
In this paper, we propose a procedure to build bivariate box plots (BBP). We first obtain the theoretical BBP for a random vector (X, Y). They are based on the univariate box plot of X and the conditional quantile curves of Y|X. They can be computed from the copula of (X, Y) and the marginal distributions. The main advantage of these BBP is that the coverage probabilities of the regions are distribution-free. So they can be selected by the users with the desired probabilities and they can be used to perform fit tests. Three reasonable options are proposed. They are illustrated with two examples from a normal model and an exponential model with a Clayton copula. Moreover, several methods to estimate the theoretical BBP are discussed. The main ones are based on linear and non-linear quantile regression. The others are based on empirical estimators and parametric and non-parametric (kernel) copula estimations. All of them can be used to get empirical BBP. Some extensions for the multivariate case are proposed as well.
Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for assessing causal compatibility is in the presence of partial information; i.e. when some of the variables are hidden/latent. This paper introduces the possible worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called a possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency.
While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, markers measuring immune response to vaccination were strongly correlated with infection. This finding generated the hypothesis that some marker-defined vaccinated subgroups were partially protected whereas others had their risk increased. This hypothesis can be assessed using the principal stratification framework (Frangakis and Rubin, 2002) for studying treatment effect modification by an intermediate response variable, using methods in the sub-field of principal surrogate (PS) analysis that studies multiple principal strata. Unfortunately, available methods for PS analysis require an augmented study design not available in HVTN 505, and make untestable structural risk assumptions, motivating a need for more robust PS methods. Fortunately, another sub-field of principal stratification, survivor average causal effect (SACE) analysis (Rubin, 2006) – which studies effects in a single principal stratum – provides many methods not requiring an augmented design and making fewer assumptions. We show how, for a binary intermediate response variable, methods developed for SACE analysis can be adapted to PS analysis, providing new and more robust PS methods. Application to HVTN 505 supports that the vaccine partially protected individuals with vaccine-induced T-cells expressing certain combinations of functions.
In this paper, we construct new valuation schemes for the liabilities and economic capital of insurance companies. Specifically, we first build a ‘SAHARA’ valuation framework based on Symmetric Asymptotic Hyperbolic Absolute Risk Aversion utility functions. Then, we construct a ‘SAHARA-CPT’ framework that incorporates the previous utility function as a value function and that is based on Cumulative Prospect Theory. The process used for assessing a life insurance company’s own funds consists in replacing the market-consistent parametrization with a utility-consistent parametrization that accounts for the risk aversion of the market and the long-term duration of the company’s commitments. Our illustrations show that this approach leads to a lower value of the Own Risk and Solvency Assessment and to a lower volatility of own funds. The framework that is based on cumulative prospect theory has the advantage over the expected utility theory framework that it considers a precautionary overweighting of extreme events, as a tradeoff for additional model complexity.
This paper addresses the issue of measuring tolerance, viewed as a multifaceted phenomenon involving several different social domains. We develop a multidimensional index for Likert-scale data, characterized by the following features: (i) it reflects the individual’s intensity of tolerant attitudes towards each social domain; (ii) the index can be broken down by dimension in order to determine the contribution of each dimension to overall tolerance; (iii) the index combines the different dimensions of tolerance using a weighted scheme that reflects the importance of each dimension in determining the overall level of tolerance. To show how this new measure of tolerance works in practice, we carry out a case study using an Italian recent survey asking the opinion of university students about different subjects, such as interreligious dialog, women/religion relationship, religion/death relationship, homosexuality, and multicultural society.
This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by . The first approach is a random walk Metropolis-Hastings (RW-MH) algorithm, the second one is a random blocking random walk Metropolis-Hastings algorithm (RBRW-MH). Both approaches are Markov chain Monte Carlo methods and can cope with ˛at priors. We carry out simulation studies to determine and compare the efficiency of the algorithms. We present an empirical illustration where GPUCs are used to nonparametrically describe the dependence of exchange rate changes of the crypto-currencies Bitcoin and Ethereum.