François Le Grand

Comparative risk aversion: A formal approach with applications to saving behavior

We consider a formal approach to comparative risk aversion and apply it to intertemporal choice models. This allows us to ask whether standard classes of utility functions, such as those inspired by Kihlstrom and Mirman (1974) [16], Selden (1978) [27], Epstein and Zin (1989) [10] and Quiggin (1982) [25] are well ordered in terms of risk aversion. Moreover, opting for this model-free approach allows us to establish new general results on the impact of risk aversion on savings behaviors. In particular, we show that risk aversion enhances precautionary savings, clarifying the link that exists between the notions of prudence and risk aversion.

Prices and volumes of options: A simple theory of risk sharing when markets are incomplete

We present a simple theory of business-cycle movements of option prices and volumes. This theory relies on time-varying heterogeneity between agents in their demand for insurance against aggregate risk. Formally, we build an infinite-horizon model where agents face an aggregate risk, but also different levels of idiosyncratic risk. We manage to characterize analytically a general equilibrium in which positive quantities of derivatives are traded. This allows us to explain the informational content of derivative volumes over the business cycle. We also carry out welfare analysis with respect to the introduction of options, which appears not to be Pareto-improving.

Too Risk Averse to Purchase Insurance? A Theoretical Glance at the Annuity Puzzle

This paper suggests a new explanation for the low level of annuitization, which is valid even if one assumes perfect markets. We show that, as soon there exists a positive bequest motive, sufficiently risk averse individuals should not purchase annuities. A model calibration accounting for temporal risk aversion generates a willingness-to-pay for annuities, which is significantly smaller than the one generated by a standard Yaari (1965) model. Moreover, the calibration predicts that riskless savings finances one third of consumption, in line with empirical findings.

On Monotone Recursive Preferences

We explore the set of preferences defined over temporal lotteries in an infinite horizon setting. We provide utility representations for all preferences that are both recursive and monotone. Our results indicate that the class of monotone recursive preferences includes Uzawa–Epstein preferences and risk‐sensitive preferences, but leaves aside several of the recursive models suggested by Epstein and Zin (1989) and Weil (1990). Our representation result is derived in great generality using Lundbergs (1982, 1985) work on functional equations.

A Robust Approach to Risk Aversion: Disentangling Risk Aversion and Elasticity of Substitution without Giving Up Preference Monotonicity

We formalize the notion of monotonicity with respect to first-order stochastic dominance in the context of preferences defined over the set of temporal lotteries. It is shown that the only Kreps and Porteus (1978) preferences which are both stationary and monotone are Uzawa preferences and risk-sensitive preferences introduced by Hansen and Sargent (1995). We also extend our results to smooth recursive ambiguity models. Focusing on monotone preferences enables a much better understanding of the role of risk aversion. As an application, we derive new general results on the determinants of precautionary savings and asset prices in dynamic settings.

Household Finance and the Value of Life

We analyze life-cycle saving strategies with a recursive model that is designed to provide reasonable positive values for the value of a statistical life. With a positive value of life, risk aversion amplifies the impact of uncertain survival on the discount rate, and thus reduces savings. Our model also predicts that risk aversion lowers stock market participation and leads to choose more conservative portfolios.

Optimal dynamic regimens with artificial intelligence: The case of temozolomide

We determine an optimal protocol for temozolomide using population variability and dynamic optimization techniques inspired by artificial intelligence. We use a Pharmacokinetics/Pharmacodynamics (PK/PD) model based on Faivre and coauthors (Faivre, et al., 2013) for the pharmacokinetics of temozolomide, as well as the pharmacodynamics of its efficacy. For toxicity, which is measured by the nadir of the normalized absolute neutrophil count, we formalize the myelosuppression effect of temozolomide with the physiological model of Panetta and coauthors (Panetta, et al., 2003). We apply the model to a population with variability as given in Panetta and coauthors (Panetta, et al., 2003). Our optimization algorithm is a variant in the class of Monte-Carlo tree search algorithms. We do not impose periodicity constraint on our solution. We set the objective of tumor size minimization while not allowing more severe toxicity levels than the standard Maximum Tolerated Dose (MTD) regimen. The protocol we propose achieves higher efficacy in the sense that –compared to the usual MTD regimen– it divides the tumor size by approximately 7.66 after 336 days –the 95% confidence interval being [7.36–7.97]. The toxicity is similar to MTD. Overall, our protocol, obtained with a very flexible method, gives significant results for the present case of temozolomide and calls for further research mixing operational research or artificial intelligence and clinical research in oncology.

Risk Aversion and Precautionary Savings in Dynamic Settings

We study how risk aversion affects precautionary savings when considering monotone recursive Kreps-Porteus preferences. In a general infinite-horizon setting, we prove that risk aversion unambiguously increases precautionary savings. The result is derived without specifying income uncertainty, which can follow any kind of stochastically monotone process, and accounting for possibly binding borrowing constraints.

Optimizing immune cell therapies with artificial intelligence

PURPOSE We determine an optimal injection pattern for anti-vascular endothelial growth factor (VEGF) and for the combination of anti-VEGF and unlicensed dendritic cells. METHODS We rely on the mathematical model of Soto-Ortiz and Finley (2016) for the interactions between the tumor growth, angiogenesis and immune system reactions. Our optimization algorithm belongs to the class of Monte-Carlo tree search algorithms. The objective consists in finding the minimal total drug doses for which an injection pattern yields tumor eradication. RESULTS Our results are twofold. First, optimized injection protocols enable to significantly reduce the total drug dose for tumor elimination. For instance, for an early diagnosis date, a total dose equal to 58% of the standard anti-VEGF dose enables to eliminate the tumor. In the case of drug combination, associating 25% of the total standard anti-VEGF dose to 10% of the dendritic cell total standard dose eradicates tumor. Our second result is that administering a dose equal to the maximal standard dose allows for later diagnosis date compared to standard protocol. For instance, in the case of anti-VEGF injection, the optimal protocol postpones the maximal diagnosis date by more than one month. CONCLUSIONS Overall, our optimization based on artificial intelligence delivers significant gains in total drug administration or in the length of the therapeutic window. Our method is flexible and could be adapted to other drug combinations.

A Comment on Two Recent Contributions on the Value of Life

Two recent articles (Córdoba and Ripoll, 2017; Hugonnier, Pelgrin, and St-Amour, 2013) have proposed a recursive formulation of utility functions combining a positive value of life, preference homotheticity, and a constant elasticity of substitution. However, when the elasticity of substitution is below one and mortality rates take plausible values, the recursive formulation admits only a unique, constant solution where utility equals zero everywhere. Non-constant solutions may only exist if mortality rates are assumed to remain low at all ages, that is, in a world of perpetually young agents. Such solutions are therefore unsuitable for studying the value of life in realistic settings. In addition, these non-constant solutions exhibit the questionable property that consumption at a given age and survival at that same age are substitutes instead of complements. We conclude this clarifying paper by reviewing various recursive specifications that can be used to study the value of life without facing such problems.