François Louis Le Grand


Last Name

Le Grand

First Name

François Louis

ORCID

0000-0002-1505-5851

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2010 - 2019252020 - 20247
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Publications 1 - 10 of 32
  • Perron–Frobenius theory recovers more than you might think: The example of limited participation
    Item type: Journal Article
    Le Grand, François Louis (2019)
    Economics Letters
  • A Comment on Two Recent Contributions on the Value of Life
    Item type: Working Paper
    Bommier, Antoine; Harenberg, Daniel; Le Grand, François Louis (2016)
    SSRN
    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.
  • A class of tractable incomplete-market models for studying asset returns and risk exposure
    Item type: Journal Article
    Le Grand, François Louis; Ragot, Xavier (2018)
    European Economic Review
  • Recursive Preferences and the Value of Life. Theory and Application to Epidemics
    Item type: Working Paper
    Bommier, Antoine; Le Grand, François Louis; Harenberg, Daniel (2024)
    This article investigates how recursive preferences can be used in the context of lifecycle models featuring uncertain and endogenous lifespans. We provide representation results showing how recursive preferences may be homothetic or fulfill a simple form of monotonicity with respect to first-order stochastic dominance, also known as ordinal dominance. While homotheticity appears to be very restrictive, constraining the intertemporal elasticity of substitution to be greater than one and risk aversion to be less than one, ordinal dominance points to the risk-sensitive preferences of Hansen and Sargent (1995), on which we focus in the second part of the paper. We then discuss the theoretical impact of risk aversion, and illustrate the relevance of our findings by looking at the consumption-mortality trade-offs faced by a benevolent planner during a pandemic.
  • Too risk averse to purchase insurance?
    Item type: Journal Article
    Bommier, Antoine; Le Grand, François Louis (2014)
    Journal of Risk and Uncertainty
    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 is a positive bequest motive, sufficiently risk averse individuals should not purchase annuities. A model calibration accounting for lifetime risk aversion generates a significantly smaller willingness-to-pay for annuities than the one generated by a standard time-additive model. Moreover, the calibration predicts that riskless savings finance one third of consumption, in line with empirical findings.
  • Optimizing immune cell therapies with artificial intelligence
    Item type: Journal Article
    Houy, Nicolas; Le Grand, François Louis (2019)
    Journal of Theoretical Biology
  • Existence of equilibria in exhaustible resource markets with economies of scale and inventories
    Item type: Journal Article
    Bommier, Antoine; Bretschger, Lucas; Le Grand, François Louis (2017)
    Economic Theory
    The paper proves the existence of equilibrium in non-renewable resource markets when extraction costs are non-convex and resource storage is possible. Inventories flatten the consumption path and eliminate price jumps at the end of the extraction period, so that market equilibrium becomes possible. We distinguish between two types of solutions, one with immediate and one with delayed buildup of inventories. For both cases, we do not only characterize potential optimal paths but also show that equilibria actually exist under fairly general conditions. It is found that optimum resource extraction involves increasing quantities over a period of time. What is generally interpreted as an indicator of increasing resource abundance is thus perfectly compatible with constant resource stocks.
  • Optimal dynamic regimens with artificial intelligence: The case of temozolomide
    Item type: Journal Article
    Houy, Nicolas; Le Grand, François Louis (2018)
    PLoS ONE
    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.
  • Optimizing treatment combination for lymphoma using an optimization heuristic
    Item type: Journal Article
    Houy, Nicolas; Le Grand, François Louis (2019)
    Mathematical Biosciences
  • A Robust Approach to Risk Aversion
    Item type: Working Paper
    Bommier, Antoine; Le Grand, François Louis (2014)
    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.
Publications 1 - 10 of 32