Financial inverse problem and reconstruction of infinitely divisible distributions with Gaussian component (Q1761432)

A risk-neutral price process \(S=\{S_t\}_{t\in [0,T]}\) of a risky asset governed by a certain equation is studied. In this note, a geometric Lévy process \(\{S_t\}\) is considered as a risk-neutral price process [\textit{T. Fujiwara} and \textit{Y. Miyahara}, Finance Stoch. 7, No. 4, 509--531 (2003; Zbl 1035.60040)]. Considering, an inverse problem of partial integro-differential equations of market prices of call options with many maturities and strike prices for geometric Lévy processes, the well-posedness (reconstruction, uniqueness and stability) of the inverse problem among the class of infinitely divisible distributions with analyticity is shown.