Lionel Sopgoui

Postdoctoral researcher in mathematical and actuarial finance

ENSAE Paris and Institut Louis Bachelier
Paris, France

\[\begin{aligned}d\widehat H_t = (\varpi\widehat z_t-\rho\widehat H_t)d t + \bar\sigma\,d W_t - \sum_{\tau_i \leq t} \kappa_i H_{\tau_i^-} S(H_{\tau_i^-}, \upsilon_{\tau_i})\end{aligned}\]

Cybersecurity level dynamics: mean-reverting diffusion with a downward jump at each cyber incident.

Portrait of Lionel Sopgoui

Research

I build stochastic models that follow shocks from firms to the banks and insurers exposed to them: cyber epidemics through insurance portfolios, carbon prices and warming through credit portfolios, and order flow through prices.

Cyber Risk

How attacks spread between firms, and what they cost insurers and defenders.

\[Y_t=\frac{1}{N_0}\sum_{k=1}^{K}\beta_{k,t}\,kI_{k,t}\]Force of infection of the cyber epidemic

Climate Risk

How the carbon price and global warming reach firms, collateral and banks.

\[\bar c^{\,i}_t=\big(\omega^i_t+r^i_t+y^i_t\,\delta_t\big)\,e^{\gamma(T_t-T_0)}\]Effective cost per unit of output: raised by warming and by the carbon price

Market Microstructure

How order flow, liquidity and trading strategies shape prices in limit order books.

\[r_t=S_t-q_t\,\gamma\,\sigma^2\,(T-t)\]Market maker’s reservation price

Research themes and ongoing work

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