A Legendre polynomial dimension reduction followed by Tikhonov regularization reconstructs terminal option prices from noisy current data in forward-time Black-Scholes with state-dependent volatility, with stability proofs for fixed truncation.
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A method combining Legendre basis reduction in time with a Carleman-estimate-based contraction mapping reconstructs initial data for nonlinear Schrödinger equations from boundary observations, with proven stability under noise.
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Forward-Time Black-Scholes Reconstruction via Regularized Legendre Reduction
A Legendre polynomial dimension reduction followed by Tikhonov regularization reconstructs terminal option prices from noisy current data in forward-time Black-Scholes with state-dependent volatility, with stability proofs for fixed truncation.
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Inverse initial data for nonlinear Schr\"odinger equation via Carleman estimates and the contraction principle
A method combining Legendre basis reduction in time with a Carleman-estimate-based contraction mapping reconstructs initial data for nonlinear Schrödinger equations from boundary observations, with proven stability under noise.