数理ファイナンスセミナー

Math-Fi seminar on 13 May

2021.05.13 Thu up
  • Date: 13 May (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Lihu Xu (University of Macau)
  • Title: Stein’s method: stable law approximation
  • Abstract:
In this talk, we will consider the stable law approximation by Stein’s method in Wasserstein-1 distance and derive a discrepancy form of the stable type central limit theorem (CLT) under appropriate conditions. The main ingredient in the proof is by solving a Stein’s equation, decomposing fractional Laplacian and using a leave-one-out argument.  From the discrepancy form,  we can obtain the optimal convergence rate of stable CLT.

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。
 

Math-Fi seminar on 25 Mar.

2021.03.24 Wed up
  • Date: 25 Mar. (Thu.) 
  • Place: On the Web
  • Time: 16:30  – 18:00 
  • Speaker: Toshiyuki Nakayama (MUFG Bank, Ltd.)
  • Title: Convergence speed of Wong-Zakai approximation for stochastic PDEs (Joint work with Stefan Tappe)
  • Abstract: 
We talk about semi-linear stochastic differential equation (SPDE) driven by finite dimensional Brownian motion. There are a few results regarding convergence rates, such as for a second-order parabolic type (Gyöngy and Shmatkov (2006), Gyöngy and Stinga (2013)) and for the infinitesimal generator of a compact and analytic semigroup (Hausenblas(2007)).
Our goal is to establish a convergence rate without imposing restrictions on the generator, that is, the generator is allowed to be the infinitesimal generator of an arbitrary strongly continuous semigroup.
Finally, we will introduce an application example for SPDE called HJMM that appears in mathematical finance.
Today’s talk is based on a co-authored paper with Stefan Tappe “ Wong-Zakai approximations with convergence rate for stochastic partial differential equations ”, 
STOCHASTIC ANALYSIS AND APPLICATIONS 2018, VOL. 36, NO. 5, pp. 832–857.

Math-Fi seminar on 18 Mar.

2021.03.18 Thu up
  • Date : 18 Mar. (Thu.) 
  • Place: On the Web
  • Time : 16:30 – 18:00 
  • Speaker: Noufel Frikha (Paris VII)
  • Title: On Some new integration by parts formula for finance and their Monte Carlo simulation
  • Abstract:
​In this talk, I will present some new integration by parts (IBP) formulae for the marginal law at a given time maturity of killed diffusions as well as a class of stochastic volatility models with unbounded drift. Relying on a perturbation argument for Markov processes, our formulae are based on a simple Markov chain evolving on a random time grid for which we develop a tailor-made Malliavin calculus. Though such formulae could be further analyzed to study fine properties of the associated densities, our main motivation lies in their numerical approximation. Indeed, we show that an unbiased Monte Carlo path simulation method directly stems from our formulae so that it can be used in order to numerically compute with optimal complexity option prices as well as their sensitivities with respect to the initial values, the so-called Greeks, namely the Delta and Vega, for a large class of non-smooth European payoff. Numerical results are proposed to illustrate the efficiency of the method.
 
This talk is based on two joint works: with Arturo Kohatsu-Higa (Ritsumeikan university) and Libo Li (New South Wales university) on the one hand, with Junchao Chen (universit ́e de Paris) and Houzhi Li (universit ́e de Paris) on the other hand.

Math-Fi seminar on 12 Mar.

2021.03.12 Fri up
  • Date: 12 Mar. (Fri.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speakers: Ju-Yi Yen (University of Cincinatti), I-Hsun Chen (Academia Sinica), Te-Chun Wang (Academia Sinica)
  • Title: Brownian Additive Functional Averaged

Math-Fi seminar on 18 Feb.

2021.02.18 Thu up
  • Date: 18 Feb. (Thu.)
  • Place: On the Web
  • Time: 16:30  - 18:00
  • Speaker: Libo Li (University of New South Wales)
  • Title: Strong approximation of jump extended CIR and CEV processes and their mean-field extension
  • Abstract:
​In this talk, we discuss the strong approximation of jump extended CIR and CEV processes with alpha stable jumps and their mean-field extension. In particular, we discuss the Euler-Maruyama scheme, derivation of Positive Preserving schemes and finally for the mean-field extension, the propagation of chaos property and the corresponding Euler-Maruyama scheme for the particle system.

Math-Fi seminar on 21 Jan.

2021.01.21 Thu up
  • Date: 21 Jan. (Thu.) 
  • Place: On the Web 
  • Time: 16:30 – 18:00
  • Speaker: Pierre Patie (Cornell University)
  • Title: Interweaving relations
  • Abstract:
In this talk, we introduce the concept of interweaving relations as a strengthening of usual intertwining relations between Markov semigroups. We proceed by providing some  interesting applications of this new idea which includes the characterization of ergodic constants and hypercontractivity estimates for non-self-adjoint semigroups.  We illustrate these results by presenting  several examples that have emerged from the recent literature: discrete-to-continuous interacting particle models, degenerate hypoelliptic Ornstein-Uhlenbeck processes, and diffusion-to-jump  Jacobi processes.
 
This talk is based on joint works with L. Miclo and with P. Cheridito, A. Srapionyan and A. Vaidyanathan.

Math-Fi seminar on 14 Jan.

2021.01.14 Thu up
  • Date: 14 Jan. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00 
  • Speaker: Azmi Maklouf (University of Tunis El Manar)
  • Title: Error estimates for De Vylder type approximations in ruin theory
  • Abstract: 
Due to its practical use, De Vylder’s approximation of the ruin probability has been one of the most popular approximations in ruin theory and its application to insurance. Surprisingly, only heuristic and numerical evidence has supported it. Finding a mathematical estimate for its accuracy has remained an open problem, going from the original paper by De Vylder (1978) through an attempt of justification by Grandell (2000).
We carry out a mathematical and critical treatment of the problem. We more generally consider De Vylder type approximations of any order k, based on fitting the k first moments of the classical risk reserve process. Moreover, we not only deal with the ruin probability, but
also with the moments of the time of ruin, of the deficit at ruin and of the surplus before ruin.
We estimate the approximation errors in terms of the safety loading coefficient, the initial reserve and the approximation order. We show their different behaviours, and the extent to which each relative error remains small or blows up, so that one has to be careful when using this approximation. Our estimates are confirmed by numerical examples.
 

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