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Stochastic Pathways in Incomplete Markets: Volterra Processes, Stopping Times, and Path-Signatures by Edouard Motte -
Vendredi 11 septembre 2026 à 15h00 - Auditoire MORE53 - Place Montesquieu, 2 - 1348 Louvain-la-Neuve -
This thesis studies the modeling, pricing, and hedging of path-dependent risks in incomplete financial and actuarial markets. Path-dependence arises in different forms across these markets: through memory in the dynamics of financial risk factors, through the arrival of information generated by insurance portfolios, and through the dependence of financial products on the past trajectory of their underlying assets. Such features lead to non-Markovian problems and call for new mathematical approaches. The thesis develops and applies different tools to address these challenges, ranging from Volterra processes and stopping-time-based strategies to path-signatures.
The first part develops pricing and hedging methods for financial models driven by Volterra processes. It addresses partial hedging in rough volatility models through Markovian approximations and duality techniques, and introduces a tractable Volterra extension of the Stein-Stein model with stochastic interest rates, providing tractable pricing formulas and an efficient calibration framework.
The second part studies the hedging of equity-linked life insurance portfolios, where policyholder deaths generate additional non-hedgeable risks and progressively reveal information. Stopping-time-based strategies are constructed to exploit this information and improve hedging, with a particular focus on quantile and shortfall hedging.
The final part develops a signature-based approach to pricing and hedging path-dependent derivatives in the presence of temporary and permanent market impact. By lifting the problem into the space of path-signatures, the optimal solution is characterized through infinite-dimensional Riccati equations on the extended tensor algebra, yielding tractable hedging strategies for path-dependent payoffs in the presence of frictions.
Overall, the thesis develops mathematical and computational tools for addressing path-dependent risks in incomplete financial and actuarial markets, combining analytical tractability with practical approaches to pricing and risk-management.
Jury members :
Prof. Donatien Hainaut (UCLouvain) (Supervisor)
Prof. Frédéric Vrins (UCLouvain) (Chairperson)
Prof. Karim Barigou (UCLouvain) (Secretary)
Prof. Eduardo Abi Jaber (Ecole Polytechnique, Paris)
Prof. Jennifer Alonso Garcia (ULB, Bruxelles)
Pay attention : the public defense of Edouard MOTTE will also take place in the form of a videoconference
