关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Stochastic differential equations and diffusion processes

13. 벼잎선충의 약제처리 방법별 방제 효과

Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.

/pdf/multidimensional-stochastic-processes-as-rough-paths-5cpf00j8b4.pdf

Multidimensional Stochastic Processes as Rough Paths

In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous-time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Parameters estimated on the daily prices of 348 stocks of NYSE and S\&P 500, on different time windows, show consistent empirical evidence for leverageeffects. Mean-reversion effects are also detected, most markedly in crisis periods.

A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data

We study the asymptotic property of simple estimator of the parameter of a Skew Brownian Motion when one observes its positions on a fixed grid — or equivalently of a simple random walk with a bias at 0. This estimator, nothing more than the Maximum Likelihood Estimator, is based only on the number of passages of the random walk at 0. It is very simple to set up, is consistent and is asymptotically mixed normal. We believe that this simplified framework is helpful to understand the asymptotic behavior of the maximum likelihood of the Skew Brownian Motion observed at discrete times which is studied in a companion paper.

/pdf/estimation-of-the-bias-parameter-of-the-skew-random-walk-and-3uoulsnmfd.pdf

Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion

In the context of rough paths theory, 
we study the regularity 
of the Ito map with respect to the starting point, 
the coefficients and perturbation of the driving rough paths. 
In particular, we show that the Ito map
is differentiable with a Holder or Lipschitz continuous
derivatives under general hypotheses. With respect to the current literature
on the subject, our proof relies on perturbation of linear
Rough Differential Equations, and the Holder regularity of the Ito map is established.

Sensitivity of rough differential equations

This C library aims at computing and simulating various quantities and random variables related to where and when a the Brownian motion hit the boundary of an interval, a square or a rectangle. We present here the algorithms used in this library.

exitbm: a library for simulating Brownian motion's exit times and positions from simple domains

We construct a recommendation system for car insurance, to allow agents to optimize up-selling performances, by selecting customers who are most likely to subscribe an additional cover. The originality of our recommendation system is to be suited for the insurance context. While traditional recommendation systems, designed for online platforms (e.g. e-commerce, videos), are constructed on huge datasets and aim to sug- gest the next best offer, insurance products have specific properties which imply that we must adopt a different approach. Our recommendation system combines the XGBoost algorithm and the Apriori algorithm to choose which customer should be recommended and which cover to rec- ommend, respectively. It has been tested in a pilot phase of around 150 recommendations, which shows that the approach outperforms standard results for similar up-selling campaigns.
Recommendation system Up-selling Car insurance XGBoost algorithm Apriori algorithm

https://hal.inria.fr/hal-02420954/document

Antoine Lejay

Papers

A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data

Estimation of the bias parameter of the skew random walk and application to the skew Brownian motion

Sensitivity of rough differential equations

exitbm: a library for simulating Brownian motion's exit times and positions from simple domains

A Recommendation System For Car Insurance