| 主讲人 |
张瑞勋 |
简介 |
<p>Path signatures—the hierarchy of iterated integrals of a path — provide a canonical way to turn nonlinear functionals of time series into linear regressions, justified by a universal approximation theorem. This theorem, however, is only an existence result. This talk presents a line of work that closes three gaps separating it from a usable methodology in finance. First, an approximation-rate theory: for smooth functionals of Itô diffusions, the truncation error of level-K signature approximations decays at a minimax-sharp polynomial rate, so signatures act as polynomials on path space. Second, an estimation theory: we characterize when Lasso consistently selects signature features, showing that the choice between Itô and Stratonovich signatures is a statistical decision that depends on the underlying dynamics. Third, a tradability theory: every discretized Itô signature is the PnL of a self-financing trading strategy, so a single fitted linear representation of a payoff simultaneously prices (by expectation) and hedges (by replication)—yielding an interpretable, model-free hedging framework with end-to-end error guarantees and robust performance on fifteen years of S&P 500 options. Based on joint works with Xin Guo, Blanka Horvath, Wen Su, Wu Su, Binnan Wang, and Chaoyi Zhao.</p> |
