Apr 2020-Mar 2021

Math-Fi seminar on 20 Nov.

2020.11.17 Tue up
  • Date: 20 Nov. (Fri.)
  • Place: On the Web (and Tokyo Satellite Campus of Ritsumeikan University; If you would like to come to the campus, please contact us by email: ritsumeikanmathfiseminar@gmail.com )
  • Time: 19:00 – 20:00
  • Speaker: Tadashi Hayashi (Mitsubishi UFJ trust and banking)
  • Title: The existence and uniqueness of a solution to Double Barrier Backward Doubly Stochastic Differential Equations
  • Abstract:
Double barrier backward doubly stochastic differential equations (DB-BDSDEs, for short) are equations with two different directions of stochastic integrals, i.e., the equations involve both a standard “forward” stochastic integral and a “backward” stochastic integral with two mutually independent standard Brownian motions, and with two reflection barriers. This kind of equations is a joint version of backward doubly stochastic differential equations (BDSDEs, for short) and double barrier backward stochastic differential equations (DB-BSDEs, for short). The former has been introduced by Pardoux and Peng. They ave proved the connection with a class of systems of quasilinear SPDEs and the existence and uniqueness result of such PDEs. The latter has been tackled by Hamadene et al. In this talk, we try to show the outline of the proof for the existence and uniqueness of a solution to DB-BDSDEs by using the “penalization method”, so-called under appropriate conditions. At the end of this talk, we introduce our next some studies that we are tackling now.
 

Math-Fi seminar on 5 Nov.

2020.11.05 Thu up
  • Date: 5 Nov. (Thu.)
  • Place: On the Web
  • Time: 18:00 -19:30
  • Speaker: Johannes Ruf (London School of Economics and Political Science)
  • Title: Hedging with linear regressions and neural networks
  • Abstract: 
We study the use of neural networks as nonparametric estimation tools for the hedging of options. To this end, we design a network, named HedgeNet, that directly outputs a hedging strategy given relevant features as input. This network is trained to minimise the hedging error instead of  the pricing error. Applied to end-of-day and tick prices of S&P 500 and Euro Stoxx 50 options, the network is able to reduce the mean squared hedging error of the Black-Scholes benchmark significantly. We illustrate, however, that a similar benefit arises by a simple linear regression model that incorporates the leverage effect. Finally, we argue that outperformance of neural networks previously reported in the literature is most likely due to a lack of data hygiene. In particular, data leakage is sometimes unnecessarily introduced by a faulty training/test data split, possibly along with an additional ‘tagging’ of data.
(Joint work with Weiguan Wang)
 

Math-Fi seminar on 29 Oct.

2020.10.29 Thu up
  • Date: 29 Oct. (Thu.)
  • Place: On the Web
  • Time: 16:00 – 19:00
  • Speaker: Jie Yen Fan (Monash University)
  • Title: Multi-type age-structured population model
  • Abstract: 
Population process in general setting, where each individual reproduces and dies depending on the state (such as age and type) of the individual as well as the entire population, offers a more realistic framework to population modelling. Formulating the population dynamics as a measure-valued stochastic process allows us to incorporate such dependence. We describe the dynamics of a multi-type age-structured population as a measure-valued process, and obtain its asymptotics, in particular, the law of large numbers and the central limit theorem. Joint work with Kais Hamza, Peter Jagers and Fima Klebaner.

Math-Fi seminar on 22 Oct.

2020.10.22 Thu up
  • Date: 22 Oct. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Huyen Pham (Paris VII)
  • Title: Control of McKean-Vlasov systems and applications
  • Abstract: 
This lecture is concerned with the optimal control of McKean-Vlasov equations, which has been knowing a surge of  interest since the emergence of the mean-field game theory.  Such control problem corresponds to the asymptotic formulation of a N-player cooperative game under mean-field interaction, and can also be viewed as an influencer strategy problem over an interacting large population. It finds various applications in economy, finance, or social sciences for modelling motion of socially interacting individuals and herd behavior.  It is also relevant for dealing with intermittence questions arising typically in risk management.
In the first part,  I will focus on the discrete-time case,  which extends the theory of Markov decision processes (MDP) to the mean-field interaction context.  We give an application with explicit results to a problem of targeted advertising via social networks.
The second part is devoted to the continuous-time framework. We shall first consider the important class of linear-quadratic McKean-Vlasov (LQMKV) control problem, which provides a major source for examples and applications. We show a direct and elementary method for solving explicitly LQMKV based on a mean version of the well-known martingale optimality principle in optimal control, and the completion of squares technique.  Next, we present the dynamic programming approach (in other words, the time consistency approach) for the control of general McKean-Vlasov dynamics. In particular, we introduce the recent mathematical tools that have been developed in this context : differentiability in the Wasserstein space of  probability measures, Itô formula along a flow of probability measures and Master Bellman equation. Some extensions to common noise, partial observation, stochastic differential games of McKean-Vlasov type are also discussed.

Math-Fi seminar on 15 Oct.

2020.10.15 Thu up
  • Date : 15 Oct. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Takis Konstantopoulos (University of Liverpool)
  • Title: Longest paths in directed random graphs

Math-Fi seminar on 8 Oct.

2020.10.08 Thu up
  • Date: 8 Oct. (Thu.)
  • Place: On the Web
  • Time: 16:30 - 18:00 
  • Speaker: Haiha Pham (Ho-chi-minh International University)
  • Title: Distribution and asymptotic results for Japanese double -debt risk model
  • Abstract: 
Inspired by double debt problem in Japan where the morgagor has to pay the remain loan even their morgage was destroyed by castastrophic disaster,  we model morgarate loan to estimate risk of the lender by a renewal – reward process. We analyse the asymptotic behavior distribution of first hitting time which represents  the probability of full repayment. We show that finite -time probability of full repayment converges exponentially fast to the infinite – time one. In a few concrete scenarios, we calculate the exact form of the infinite-time probability and the corresponding premiums.
 

Math-Fi seminar on 24 Sep.

2020.09.24 Thu up
  • Date: 24 Sep. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Alex Mijatovic (University of Warwick)
  • Title: Invariance principle for non-homogeneous random walks
  • Abstract:
We discuss an invariance principle for a class of zero-drift spatially non-homogeneous random walks in ℝ^d, which may be recurrent in any dimension. The limit X is an elliptic martingale diffusion, which may be point-recurrent at the origin for any d≥2. To characterize X, we introduce a (non-Euclidean) Riemannian metric on the unit sphere in ℝ^d and use it to express a related spherical diffusion as a Brownian motion with drift. This representation allows us to establish the skew-product decomposition of the excursions of X and thus develop the excursion theory of X without appealing to the strong Markov property. This leads to the uniqueness in law of the stochastic differential equation for X in ℝ^d, whose coefficients are discontinuous at the origin. Using the Riemannian metric we can also detect whether the angular component of the excursions of X is time-reversible. If so, the excursions of X in ℝ^d generalize the classical Pitman–Yor splitting-at-the-maximum property of Bessel excursions. This is joint work with N. Georgiou and A. Wade.

Math-Fi seminar on 17 Sep.

2020.09.17 Thu up
  • Date: 17 Sep. (Thu.) 
  • Place: On the Web
  • Time: 17:00 – 18:30 
  • Speaker: Stephane Menozzi
  • Title: Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift
 

Math-Fi seminar on 10 Sep.

2020.09.17 Thu up
  • Date: 10 Sep.  (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Ngo Hoang Long (Hanoi National University of Education)
  • Title: Tamed-adaptive Euler-Maruyama approximation for  SDEs with locally Lipschitz continuous drift and locally H\”older continuous diffusion coefficients
  • Abstract: 
We propose a tamed-adaptive Euler-Maruyama approximation scheme for stochastic differential equations with locally Lipschitz continuous, polynomial growth drift, and locally H\”older continuous, polynomial growth diffusion coefficients. We consider the strong convergence and stability of the new scheme. In particular, we show that under some sufficient conditions for the stability of the exact solution,  the tamed-adaptive scheme converges strongly in any infinite time interval.
This is joint work with LUONG Duc Trong and KIEU Trung Thuy.

Math-Fi seminar on 3 Sep.

2020.09.03 Thu up
  • Date: 3 Sep. (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Linglong Yuan (University of Liverpool)
  • Title: Limit theorems for continuous-state branching processes with immigration
  • Abstract: 
The continuous-state branching processes with immigration (CBI) arises in the literature of stochastic processes with a biological background.
Kawazu and Watanabe (1971) firstly introduced CBI and proved that it is the limit of a sequence of Galton-Waton discrete branching processes with immigration.
Since then CBI has received a lot of attention. It is connected to stochastic differential equations, Levy processes, population modelling etc. In mathematical finance, a special kind of CBI is called Cox–Ingersoll–Ross model which is well known to describe the evolution of interest rates. In this talk, we will briefly introduce CBI and focus on the long term behavior which turn out to have two different regimes. In the first one, an almost sure convergence is proved adapting the Grey’s martingale.
In the second one, only convergence in law is possible and a different technique is needed. Our results provide a global picture on the long term behavior and corrected a misprint in Pinsky’s paper [Bull. Amer. Math. Soc. 78 (1972), 242-244].
This talk is based on a joint work with Clement Foucart, Chunhua Ma.
 

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