2021年度

Math-Fi seminar on 22 Apr.

2021.04.21 Wed up
  • Date: 22 Apr. (Thu.) 
  • Place: On the Web 
  • Time: 16:30 – 18:00
  • Speaker: Jorge González Cázares (University of Warwick)
  • Title: Recovering Brownian and jump parts from high-frequency observations of a Lévy process
  • Abstract:
We introduce two general non-parametric methods for recovering paths of the Brownian and jump components from high- frequency observations of a Lévy process, both methods yield the same polynomial rate of convergence dependent on the  Blumenthal-Getoor index. The first procedure relies on reordering of independently sampled normal increments and thus avoids tuning parameters. The functionality of this method is a consequence of the small time predominance of the Brownian component, the presence of exchangeable structures, and fast convergence of normal empirical quantile functions. The second procedure  filters the increments and compensates with the final value, requiring a carefully chosen threshold.

Math-Fi seminar on 15 Apr.

2021.04.15 Thu up
  • Date: 15 Apr. (Thu.) 
  • Place: On the Web 
  • Time: 16:30 – 18:00
  • Speaker: Tai-Ho Wang (Baruch College)
  • Title: Dynamic optimal execution under price impact with inventory cost: a heterogeneous characteristic time scales approach
  • Abstract:
We generalize the classical Almgren-Chriss model of price impact by adding an extra feature that models the market makers’ impact to the transaction price by aggregated Ornstein-Uhlenbeck processes. During execution of a meta order, market makers are assumed to mean revert their positions to certain preassigned capacities. Once the execution terminates, the market makers revert their positions back to zero. The expected price path post TWAP (time weighted average price) execution reverts to a price level higher than price before the TWAP execution. Should there be no contribution from the market maker, the model recovers the classical Almgren-Chriss model. The execution problem faced by investor can be recast as a possibly infinite dimensional stochastic control problem, which in general is neither Markovian nor semimartingale. However, the problem remains linear-quadratic, as a result, we are able to derive, and consequently obtain the optimal trading strategies, a system of Riccati equations that characterizes the value function of the stochastic control problem. Numerical examples will be presented to illustrate the implementation of the resulting optimal execution strategy under the proposed model.
The talk is based on a joint work with Xue Cheng and Marina Di Giacinto.

Math-Fi seminar on 9 Apr.

2021.04.08 Thu up
  • Date: 9 Apr. (Fri.) 
  • Place: On the Web 
  • Time: 16:30 – 18:00
  • Speaker: Tomonori Nakatsu
  • Title: Stochastic delay equationの解の密度関数の評価と伊藤Taylor展開
  • Abstract:
本発表ではまず、Stochastic delay equationの解の密度関数の下からの評価に関する結果を紹介する。次に、Stochastic delay equationに対する伊藤Taylor展開について述べる。両トピックは独立した内容であるが、ともにMalliavin解析が重要な役割を果たす。
 

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