arXiv subjects

Arthur Bourdon

Publications and source records attributed to Arthur Bourdon.

3 recordsLinked to original sources

arXiv2026

Approximation of stochastic insurer balance-sheet results using signatures of economic scenarios

In the insurance industry, Asset and Liability Management (ALM) models are key tools for numerous applications, including Solvency Capital Requirement (SCR) computation and asset allocation optimization. However, their use often entails a significant computational cost, especially when a large number of sensitivities or stressed balance-sheet evaluations must be performed. In this work, we propose an approximation framework for the outputs of an ALM model, such as the Value In Force or the Best Estimate, based on the theory of path signatures. More precisely, the proposed approach consists of approximating ALM outputs by a linear combination of signature terms derived from input economic scenarios. We show that the resulting surrogate is easy to calibrate, essentially through regularized linear regression, and exhibits strong predictive performance while drastically reducing computational costs. We further investigate its robustness under changes in the distribution of economic scenarios by considering variations in the parameters of the underlying model of risk factors while the surrogate model is kept fixed. These results make the proposed approach particularly suitable for large-scale sensitivity analyses and fast balance-sheet evaluations in practical actuarial applications.

q-fin.RM↗

arXiv2026

Moments in Rough Bergomi and Boundary Attainment in Rough Heston

We study two probabilistic questions for stochastic Volterra equations arising in rough volatility. These equations underlie some of the most popular non-Markovian stochastic volatility models in mathematical finance. First, we establish subcritical positive moment bounds for stochastic exponentials driven by Gaussian Volterra processes. In the Gaussian Volterra-Bergomi setting, we prove that if $\rho\in[-1,0)$, then $\mathbb{E}[S_T^p]<\infty$ for every $0<p<p_\rho$, where $p_{-1}=\infty$ and $p_\rho=(1-\rho^2)^{-1}$ for $-1<\rho<0$. For the fractional rough Bergomi kernel, we additionally prove explosion at the critical exponent $p=p_\rho$. Combined with the known explosion above the threshold, this yields the exact criterion $\mathbb{E}[S_T^p]<\infty$ if and only if $0<p<p_\rho$ in the fractional rough Bergomi model. Second, for the fractional Volterra square-root process, equivalently the rough Heston variance process, we prove that its law has a positive atom at zero at every positive time. In particular, no Feller-type condition can make the zero boundary inaccessible in the fractional rough Heston regime.

math.PR↗

arXiv2026

Linear independence properties of the signature components of time-augmented stochastic processes

Adding the time as a component of a stochastic process before computing its signature terminal value ensures injectivity and supports universal approximation results, but it induces linear dependence among the components of the signature terminal value. For any natural number $N$, the terminal values of the signature components associated with words of length not greater than $N$ are the image of the terminal values of the signature components associated with words of length $N$ by some universal linear map. We generalize this result by exhibiting other subfamilies of components -- represented by subfamilies of words -- with the same representation property. When considering the signature of the solution to a stochastic differential equation with a uniformly elliptic diffusion coefficient, we show that any such subfamily of components is linearly independent for the almost-sure equality and therefore provides a basis of the linear span of all components associated with words of length not greater than $N$. The linear independence of these subfamilies is preserved for the affine interpolation of this solution on a grid with a sufficiently small time step. We characterize bases of components with minimal computation cost. Finally, we remark that the subfamilies of words obtained above share a similar representation property when applied to the time-augmented EFM signature. For a Brownian semimartingale with a non-degenerate diffusion coefficient, we show that any such subfamily of components of its time-augmented EFM signature is almost-surely linearly independent for the $dt$-a.e. equality.

math.PR↗