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# Search by event  2255 | enregistrements trouvés : 15

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## Multi angle  Quasi-Monte Carlo methods and applications: introduction Tichy, Robert (Auteur de la Conférence) | CIRM (Editeur )

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## Virtualconference  PDMPs in risk theory and QMC integration III Thonhauser, Stefan (Auteur de la Conférence) | CIRM (Editeur )

This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential equations. Unfortunately, only particular parameter constellations allow for closed form solutions such that in general one needs to rely on numerical methods. Instead of studying these associated integro-differential equations, we adapt the problem in a way that allows us to apply deterministic numerical integration algorithms such as QMC rules.
This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential ...

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## Virtualconference  On the estimation of conditional quantiles - lecture 3 Maume-Deschamps, Véronique (Auteur de la Conférence) | CIRM (Editeur )

Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis (QOSA). QOSA indices are relevant in order to quantify uncertainty on quantiles, for example in insurance operational risk contexts. We shall present several view points on conditional quantile estimation: quantile regression and improvements, Kernel based estimation, random forest estimation. We shall focus on applications to QOSA.
Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis ...

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## Virtualconference  On the estimation of conditional quantiles - lecture 2 Maume-Deschamps, Véronique (Auteur de la Conférence) | CIRM (Editeur )

Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis (QOSA). QOSA indices are relevant in order to quantify uncertainty on quantiles, for example in insurance operational risk contexts. We shall present several view points on conditional quantile estimation: quantile regression and improvements, Kernel based estimation, random forest estimation. We shall focus on applications to QOSA.
Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis ...

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## Virtualconference  Optimizing dividends and limited capital injections via exponential approximations I Avram, Florin (Auteur de la Conférence) | CIRM (Editeur )

The recent papers Gajek-Kucinsky (2017), Avram-Goreac-LiWu (2020) investigated the control problem of optimizing dividends when limiting capital injections by bankruptcy is taken into consideration. The first paper works under the spectrally negative Levy model; the second works under the Cramer-Lundberg model with exponential jumps, where the results are considerably more explicit.
The first talk extends, exploiting the W-Z scale functions, results of Gajek-Kucinsky (2017) to the case when a final penalty is taken into consideration as well. This requires the introduction of new scale and Gerber-Shiu functions.
The second talk illustrates the fact that quite reasonable approximations of the general problem may be obtained using the exponential particular case studied in Avram-Goreac-LiWu (2020). We start by experimenting with de Vylder type approximations for the scale function $W_q(x)$; this amounts essentially to replacing our process by one with exponential jumps and cleverly crafted parameters based on the first three moments of the claims. We show that very good approximations may be obtained for two fundamental objects of interest: the growth exponent $\Phi_q$ of the scale function $W_q(x)$, and the (last) global minimum of $W_q'(x)$, which is fundamental in the de Finetti barrier problem. Turning then to the dividends and limited capital injections problem, we show that a new exponential approximation specific to this problem achieves very good results: it consists in plugging into the objective function for exponential claims the exact "non-exponential ingredients" (scale functions and, survival and mean functions) of our non-exponential examples.
The recent papers Gajek-Kucinsky (2017), Avram-Goreac-LiWu (2020) investigated the control problem of optimizing dividends when limiting capital injections by bankruptcy is taken into consideration. The first paper works under the spectrally negative Levy model; the second works under the Cramer-Lundberg model with exponential jumps, where the results are considerably more explicit.
The first talk extends, exploiting the W-Z scale functions, ...

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## Virtualconference  Number sequences for simulation - lecture 1 Ökten, Giray (Auteur de la Conférence) | CIRM (Editeur )

After an overview of some approaches to define random sequences, we will discuss pseudorandom sequences and low-discrepancy sequences. Applications to numerical integration, Koksma-Hlawka inequality, and Niederreiter’s uniform point sets will be discussed. We will then present randomized quasi-Monte Carlo sequences.

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## Virtualconference  Two concrete FinTech applications of QMC Larcher, Gerhard (Auteur de la Conférence) | CIRM (Editeur )

I present the basics and numerical result of two (or three) concrete applications of quasi-Monte-Carlo methods in financial engineering. The applications are in: derivative pricing, in portfolio selection, and in credit risk management.

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## Virtualconference  Brief introduction of Quasi-Monte Carlo Methods and their Applications Leobacher, Gunther (Auteur de la Conférence) | CIRM (Editeur )

In the first part, we briefly recall the theory of stochastic differential equations (SDEs) and present Maruyama's classical theorem on strong convergence of the Euler-Maruyama method, for which both drift and diffusion coefficient of the SDE need to be Lipschitz continuous.

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## Virtualconference  On the estimation of conditional quantiles - lecture 1 Maume-Deschamps, Véronique (Auteur de la Conférence) | CIRM (Editeur )

Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis (QOSA). QOSA indices are relevant in order to quantify uncertainty on quantiles, for example in insurance operational risk contexts. We shall present several view points on conditional quantile estimation: quantile regression and improvements, Kernel based estimation, random forest estimation. We shall focus on applications to QOSA.
Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis ...

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## Virtualconference  The coordinate sampler: a non-reversible Gibbs-like MCMC sampler Robert, Christian P (Auteur de la Conférence) | CIRM (Editeur )

In this talk, we derive a novel non-reversible, continuous-time Markov chain Monte Carlo (MCMC) sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process (PDMP), which can be seen as a variant of the Zigzag sampler. In addition to proving a theoretical validation for this new sampling algorithm, we show that the Markov chain it induces exhibits geometrical ergodicity convergence, for distributions whose tails decay at least as fast as an exponential distribution and at most as fast as a Gaussian distribution. Several numerical examples highlight that our coordinate sampler is more efficient than the Zigzag sampler, in terms of effective sample size.
[This is joint work with Wu Changye, ref. arXiv:1809.03388]
In this talk, we derive a novel non-reversible, continuous-time Markov chain Monte Carlo (MCMC) sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process (PDMP), which can be seen as a variant of the Zigzag sampler. In addition to proving a theoretical validation for this new sampling algorithm, we show that the Markov chain it induces exhibits geometrical ergodicity convergence, for distributions whose tails decay at ...

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## Virtualconference  Risk theory: models and objectives PDMPs in risk theory and QMC integration I Thonhauser, Stefan (Auteur de la Conférence) | CIRM (Editeur )

This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential equations. Unfortunately, only particular parameter constellations allow for closed form solutions such that in general one needs to rely on numerical methods. Instead of studying these associated integro-differential equations, we adapt the problem in a way that allows us to apply deterministic numerical integration algorithms such as QMC rules.
This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential ...

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## Virtualconference  Derivative pricing, simulation from non-uniform distributions - lecture 3 Ökten, Giray (Auteur de la Conférence) | CIRM (Editeur )

The models of Bachelier and Samuelson will be introduced. Methods for generating number sequences from non-uniform distributions, such as inverse transformation and acceptance rejection, as well as generation of stochastic processes will be discussed. Applications to pricing options via rendomized quasi-Monte Carlo methods will be presented.

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## Virtualconference  PDMPs and Integrals PDMPs in risk theory and QMC integration II Thonhauser, Stefan (Auteur de la Conférence) | CIRM (Editeur )

This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential equations. Unfortunately, only particular parameter constellations allow for closed form solutions such that in general one needs to rely on numerical methods. Instead of studying these associated integro-differential equations, we adapt the problem in a way that allows us to apply deterministic numerical integration algorithms such as QMC rules.
This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential ...

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## Virtualconference  Number sequences for simulation - lecture 2 Ökten, Giray (Auteur de la Conférence) | CIRM (Editeur )

After an overview of some approaches to define random sequences, we will discuss pseudorandom sequences and low-discrepancy sequences. Applications to numerical integration, Koksma-Hlawka inequality, and Niederreiter’s uniform point sets will be discussed. We will then present randomized quasi-Monte Carlo sequences.

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## Virtualconference  Stochastic differential equations Leobacher, Gunther (Auteur de la Conférence) | CIRM (Editeur )

In the second part we show how the classical result can be used also for SDEs with drift that may be discontinuous and diffusion that may be degenerate. In that context I will present a concept of (multidimensional) piecewise Lipschitz drift where the set of discontinuities is a sufficiently smooth hypersurface in the multi-dimensional euclidean space. We discuss geometric properties of the set of discontinuities that are needed to transfer the convergence result from the Lipschitz case to the piecewise Lipschitz case.
In the second part we show how the classical result can be used also for SDEs with drift that may be discontinuous and diffusion that may be degenerate. In that context I will present a concept of (multidimensional) piecewise Lipschitz drift where the set of discontinuities is a sufficiently smooth hypersurface in the multi-dimensional euclidean space. We discuss geometric properties of the set of discontinuities that are needed to transfer the ...

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