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Actuarial science lies at the intersection of probability, finance, risk measurement, and decision-making under uncertainty. For insurers, the central challenge is not only to assess future losses, but also to determine how much capital is required, how assets should be allocated, how liabilities should be valued, and how risk should be managed in the presence of regulatory and economic constraints.
My research in this area addresses several of these core actuarial problems. It includes asset allocation under liability, withdrawal, and solvency constraints; the analysis of ruin probabilities and classical risk models; decision-making based on distortion risk measures and ambiguity aversion; and the valuation of insurance liabilities and capital margins within stochastic reserving frameworks. These topics combine theoretical results with questions that arise directly in insurance practice.
A recurring objective is to understand how uncertainty should affect actuarial decisions and how mathematical models can support a consistent balance between profitability, solvency, and policyholder protection. More broadly, this research contributes to the development of actuarial methods that remain both mathematically sound and relevant for risk management, capital allocation, and insurance regulation.
Cousin, A., Jiao, Y., Robert, C. and Zerbib, D. (2022). “Optimal asset allocation subject to withdrawal risk and solvency constraints.”
Risks, 10(1), 15.
DOI : 10.3390/risks10010015
Abstract
This paper investigates the optimal asset allocation of a financial institution whose customers are free to withdraw their capital-guaranteed financial contracts at any time. In accounting for the asset-liability mismatch risk of the institution, we present a general utility optimization problem in a discrete-time setting and provide a dynamic programming principle for the optimal investment strategies. Furthermore, we consider an explicit context, including liquidity risk, interest rate, and credit intensity fluctuations, and show by numerical results that the optimal strategy improves both the solvency and asset returns of the institution compared to a standard institutional investor’s asset allocation.
Cousin, A., Jiao, Y., Robert, C. and Zerbib, D. (2016). “Asset allocation strategies in the presence of liability constraints.”
Insurance: Mathematics and Economics, 70, 327–338.
Abstract
The performance of portfolio managers is usually assessed by comparing their allocation strategies to a benchmark portfolio. A major issue for portfolio managers of liability driven institutions is that no benchmark is given to them, although they face mid-term objectives with short term constraints. No performance attribution methodology may then be used to serve as a reference. Assessing the performance of the asset manager as an agent, represents a major stake for the institution as a principal delegating a mandate of asset management. We propose an optimal asset allocation approach taking into account liability constraints to build a benchmark. This benchmark will be used to compare the ex-post effective performance of the asset manager to the effective performance of the ex-ante optimal dynamic asset allocation.
Robert, C. (2014). “On the De Vylder and Goovaerts Conjecture About Ruin for Equalized Claims.”
Journal of Applied Probability, 51(3), 874–879.
DOI : 10.1239/jap/1409932679
Abstract
In ruin theory, the conjecture given in De Vylder and Goovaerts (2000) is an open problem about the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability evaluated in the associated model with equalized claim amounts. In this paper we consider a weaker version of the conjecture and show that the integrals of the ruin probabilities with respect to the initial risk reserve are uniformly comparable.
Robert, C. and Thérond, P.-E. (2014). “Distortion risk measures, ambiguity aversion and optimal effort.”
ASTIN Bulletin, 44(2), 277–302.
Abstract
We consider the class of concave distortion risk measures to study how choice is influenced by the decision-maker's attitude to risk and provide comparative statics results. We also assume ambiguity about the probability distribution of the risk and consider a framework à la Klibanoff, Marinacci and Mukerji (2005; A smooth model of decision making under ambiguity. Econometrica, 73, 1849–1892) to study the value of information that resolves ambiguity. We show that this value increases with greater ambiguity, with greater ambiguity aversion, and in some cases with greater risk aversion. Finally, we examine whether a more risk-averse and a more ambiguity-averse individual will invest in more effort to shift his initial risk distribution to a better target distribution.
Robert, C. (2013). “Market Value Margin calculations under the Cost of Capital approach within a Bayesian chain ladder framework.”
Insurance: Mathematics and Economics, 53(1), 216–229.
Abstract
In the Solvency II framework, insurance companies need to calculate the Best Estimate valuation of Liabilities (BEL) and the Market Value Margin (MVM) for non-hedgeable insurance-technical risks. The Cost-of-Capital approach defines the MVM as the present value of the current and future Solvency Capital Requirement (SCR) of the non-hedgeable risks to protect against adverse developments in the run-off of the insurance liabilities. However the SCR at time 𝑡 itself depends on the increase in the MVM between 𝑡 and 𝑡 +1. Hence there exists an intricate circularity dependency between both quantities. In this paper we present exact and accurate approximate analytic formulas for MVMs within a Bayesian log-normal chain ladder framework.
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