Francisco J. Vázquez

Full Insurance, Bayesian Updated Premiums, and Adverse Selection

In the classic Rothschild-Stiglitz model of adverse selection in a competitive environment, we analyse a “no-claims bonus” type contract (bonus-malus). We show that, under full insurance coverage, if the insurance company applies Bayess rule to learn about client probability types over time and uses this information in premium calculations for contract renewals, then there exist conditions under which all client types strictly prefer the Bayesian updating contract to the classic Rothschild-Stiglitz separating equilibrium.

An experiment on rational insurance decisions

We describe the results of an experiment on decision making in an insurance context. The experiment was designed to test for the underlying rationality of insurance consumers, where rationality is understood in usual economic terms. In particular, using expected utility as the preference function, we test for positive marginal utility, risk aversion, and decreasing absolute risk aversion, all of which are normal postulates for any microeconomic decision context under uncertainty or risk. We find that there the discrepancy from rational decision making increases with the sophistication of the rationality criteria, that irrationality concerning fair premium contracts is uncharacteristically high, and that the slope of absolute risk aversion seems to depend on the format of the insurance contract.

Emulation, Prevention and Social Interaction in Consumption Dynamics

In this paper we show that the role of diversity, local interactions and global endogenous change at the level of social standards might be crucial in understanding the evolution of consumption patterns in modern economies. We propose an evolutionary model from which consumption dynamics can be analyzed as global properties emerging from the endogenous transformation of a society inhabited by boundedly rational interactive consumers. This work aspires to take a modest step forward in the direction of an evolutionary theory of demand change.

A theorem on multi-period insurance contracts without commitment

Abstract In a multi-period setting that is equivalent to the classic Rothschild–Stiglitz adverse selection situation, we prove that if insurers do not gather information on accidents over time, then the inability to commit to contract renewals is sufficient for the optimal contract sequence to be periodic repetition of the Rothschild–Stiglitz single-period equilibrium.

The BDS test and delay time

One of the most popular tests for detecting non-linear structure is the BDS test. This test is based on the correlation integral, and some studies have proved the sensitivity of this concept in relation to the choice of one particular parameter: delay time. However, the BDS test considers fixed delay time equal to one. In this paper it is investigated whether a flexible choice of delay time might improve the capacity of the BDS test. It is shown that the BDS-G test (generalized BDS test, including delay time choice) can capture non-linearities that are undetected by the classical BDS test. Finally, the robustness of the BDS-G test in the presence of noise is analysed.

Dimension estimation with the BDS-G statistic

The issue of time delay has been controversial among the specialized literature. In fact, there exist some contrasted methods to choose it. It is the case that even though they are investigated for chaotic series, they fail to detect which series come from a deterministic and chaotic system. In this study a new procedure for selecting the delay time which produces good results about the estimation of the correlation dimension in chaotic series is introduced. The method is based upon a statistic (BDS-G), rooted on the integral correlation function, that takes advantage of the information contained in the data in terms of dependence, and it uses it to choose proper delay times and embedding dimensions. The results for the studied series, even for small data sets, are satisfactory.

The price of risk with incomplete knowledge on the utility function

When a risk is exchanged, the exact value for the minimum price (positive or negative) that the purchaser (investor, or insurer) is willing to pay is given by the certainty equivalent wealth level, which in turn depends on his specific utility function. When this utility function is unknown, then only a sufficient condition on the price can ever be found. This paper provides methods for calculating such a sufficient condition, when only limited information on the utility function is known.

An analysis of insurance demand in the newsboy problem

In this paper we study the standard newsboy problem, but under two new assumptions when compared to the existing literature. First, we assume that the wholesaler is an expected profit maximiser who sets the wholesale price optimally, and in doing so, takes into account the salvage value at which the newsboy can return unsold items to the wholesaler. Second, we assume that the salvage value is a choice variable of the newsboy, and in that way, it acts as a standard insurance device. The newsboy’s optimal salvage value then represents an optimal demand for insurance. We study in particular the optimal pricing problem of the wholesaler, and show that it can be expressed as a mark-up equation. We also show that insurance is provided at an actuarially unfair price. As regards the optimal demand for insurance by the newsboy, the problem is too complex for a closed form solution to be possible, so we resort to a simulation which returns the results that a strictly positive level of strictly partial insurance is demanded when the newsboy is strictly risk averse, and the optimal level of insurance coverage increases with risk aversion.

A computational consumer-driven market model: statistical properties and the underlying industry dynamics

We present an agent-based market model in which social emulation by consumers and the adaptation of producers to demand play a significant role. Our theoretical approach considers boundedly-rational agents, heterogeneity of agents and product characteristics, and the co-evolution of consumers’ desires and firms’ adaptation efforts. The model reproduces, and allows us to interpret, statistical regularities which have been observed in the evolution of industrial sectors, and that seem to be also significant in the case of discretionary consumption activities. Thus, we suggest new determinants and explanations (from the consumer-side) for these stylized facts, and we obtain new theoretical patterns which may be of help to better understand the dynamics of discretionary goods markets. This model and results may contribute to guide future research on the field of consumer market.

How information and communication technology affects decision-making on innovation diffusion: An agent-based modelling approach

We introduce a computational agent‐based model of innovation diffusion that allows us to analyse the influence of information and communication technology (ICT) development on decision‐making. Model dynamics are based on local emulation between pairs of individuals that generate an evolving social network on which an innovation is virally spread (by word of mouth). Results suggest that ICT development affects the data usefulness for decision‐making by changing the topology of the social network (the means whereby the innovation is propagated). Paradoxically, a higher level of ICT development (providing a larger volume of data) narrows the differences between better and worse launch strategies, thus reducing data‐driven decision‐making usefulness, which then shows diminishing returns on the ICT level.