Math-Fi seminar on 5 June. (Co-organized as a Quantum Walk Seminar)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 15:40–19:00
- Speaker 1: Ryoichi Suzuki (Tokyo University of Science)
- Time: 15:40–16:40
- Title: Malliavin-Mancino-Taylor type formulas and their applications to finance
- Abstract:
This presentation briefly introduces the Clark-Ocone-Haussmann (COH) formula, providing a martingale representation of random variables, and its Taylor-type extension, the Malliavin-Mancino-Taylor (MMT) formula. We then focus on developing MMT type formulas formulas for jump processes, specifically for $L^1$and $L^2$-pure jump additive processes, including versions under a change of measure. A key application is the derivation of explicit risk-minimizing hedging strategies in financial market models driven by pure jump additive processes.
These results, from joint work by M. Handa, M.E. Mancino, advance Malliavin calculus tools for finance.
- Speaker 2: Johannes Ruf (London School of Economics)
- Time: 16:50-17:50
- Title: Predictable variations in stochastic calculus
- Abstract:
The focus of this talk is the transformation of increments of a stochastic process by a predictable function. Many operations in stochastic analysis can be considered under this point of view. Stochastic integrals, for example, are linear functionals of process increments. Although mathematically equivalent, focusing on transformation of increments often leads to simpler proofs of more general statements in stochastic calculus. In this talk specifically, we illustrate how considering predictable variations lead to various Ito-type formulas.
Joint work with Ales Cerny
- Speaker 3: Tomoyuki Terada（Kanazawa Institute of Technology）
- Time: 18:00-19:00
- Title: Szegedy walkの確率測度と再帰性に関する最近の研究
- Abstract:
量子ウォークの挙動を明らかにする上で、ウォーカーの確率測度を明示的に求めることは、基本的かつ重要な問題である。本講演では、パスグラフ上のSzegedy walkに対するスペクトル解析を通じて、この確率測度を導出する手法を紹介する（今野・井手・寺田, 2023,YMJ）。具体的には、パスグラフ上のランダムウォークから誘導されるヤコビ行列の固有値および固有ベクトルを用いて、確率測度の公式を得る。パスグラフ上のランダムウォークでは、直交多項式の性質を活用し、Karlin–McGregorの公式によって確率測度が具体的に記述されることが知られているが、本研究はこれに対応する量子ウォークの結果とも言える。また、ランダムウォークおよび量子ウォークにおける再帰確率に関する最近の話題についても紹介する。
日本語
English