MSThBC25
Numerical Methods for Stochastic PDE and Uncertainty Quantification  Part IV of IV
For Part I, see MSTuE25
For Part II, see MSWeD25
For Part III, see MSWeE25
Date: August 13
Time: 10:0012:00
Room: 210A
(Note: Click title to show the abstract.)
Organizer:
ZHOU, TAO (AMSS, the Chinese Acad. of Sci.)
Yu, Xijun (Inst. of Applied Physics & Computational Mathematics)
Xiu, Dongbin (Univ. of Utah)
Abstract: Efficient solution strategy for stochastic partial differential equations (SPDE) has been a classical topic, as many physical phenomena are inherently random. The topic has received an increasing amount of attention in recent years, driven by the need for uncertainty quantification (UQ). In UQ, even deterministic systems need to be modeled as random because of the uncertainty in the system inputs. Stochastic problems become more challenging to solve, as they often reside in high dimensional random space. The purpose of this minisymposium is to gather researchers from mathematics and computer science and engineering to interchange the latest advances in simulation techniques for SPDE and UQ. The focus will be on efficient algorithms for practical systems, particularly those arising from multidisciplinary problems.
MSThBC251
10:0010:30
Stochastic Collocation Methods Via L1 Minimization Using Randomized Quadratures
GUO, LING (Department of Mathematics, Shanghai Normal Univ.)
Narayan, Akil (Univ. of Massachusetts Dartmouth)
Xiu, Dongbin (Univ. of Utah)
ZHOU, TAO (AMSS, the Chinese Acad. of Sci.)
Abstract: In this talk, we discuss the stochastic collocation methods via l1 minimization, by
randomly sampling from the corresponding tensor grid of Gaussian points. A nonintrusive algorithm is established to construct polynomial approximations for parametric functions. We provide theoretical analysis on the validity of the approach. The framework includes both the bounded and the unbounded measures. Several numerical examples are given to confirm the theoretical results and examine the efficiency of our method.
MSThBC252
10:3011:00
Graph Theoretic Models for the Solution of Stochastic Multiscale Problems
Zabaras, Nicholas (Warwick Centre for Predictive Modelling, Univ. of Warwick)
Abstract: In this presentation, we will advocate the exploration of synergies between the machine learning and uncertainty quantification research communities towards addressing the aforementioned problems. In particular, we will present a datadriven probabilistic graphical model based methodology to efficiently perform uncertainty quantification in multiscale systems. We make predictions from the probabilistic graphical model using (loopy) belief propagation algorithms.
CPThBC253
11:0011:20
Principal component analysis for multiple time series data: a symbolic data analysis approach
Wu, HanMing (Tamkang Univ.)
Abstract: This study extended the principal component analysis (PCA) to multiple time series data through a symbolic data analysis approach. Firstly the data is converted to the time dependent intervals where the interval is described by a starting value and an ending value of a time period. Then, PCA is applied to those intervals of directed segments. The proposed method is useful for exploring the insight structure and the behaviors of objects in a lowerdimensional space.
CPThBC254
11:2011:40
A ConsumptionInvestment Problem with a Diminishing Basket of Goods
Mousa, Abdelrahim (Birzeit Univ.)
Abstract: We consider the problem faced by an economic agent trying to find the optimal strategies for the joint management of her consumption from a basket of K goods that may become unavailable for consumption from some random time \tau_i onwards, and her investment portfolio in a financial market model comprised of one riskfree security and an arbitrary number of risky securities driven by a multidimensional Brownian motion. We apply previous abstract results on stochastic optimal control problem with multiple random time horizons to obtain a sequence of dynamic programming principles and the corresponding HamiltonJacobiBellman equations. We then proceed with a numerical study of the value function and corresponding optimal strategies for the problem under consideration in the case of discounted constant relative risk aversion utility functions (CRRA).
CPThBC255
11:4012:00
A backward dual representation for the quantile hedging of Bermudan options
BOUVERET, GERALDINE (IMPERIAL COLLEGE LONDON)
Abstract: We study the problem of hedging a claim of Bermudan style with a given probability p within a Markovian complete financial market.
More precisely, we want to characterize the minimal initial value v(.,p) of an hedging portfolio for which we can find a financial strategy such that, with a probability p, it remains above the exercise value of the Bermudan option at any possible exercise date.
This problem is referred to as a stochastic target and quantile hedging problem and is an extension to [1] and [2].
Using stochastic target and duality arguments, we derive a backward algorithm for the Fenchel transform of the pricing function. We provide numerical illustrations.
[1] Bruno Bouchard, Romuald Elie, and Nizar Touzi. Stochastic target problems with
controlled loss. SIAM Journal on Control and Optimization, 48(5):3123¨C3150, 2009.
[2] Hans Föllmer and Peter Leukert. Quantile hedging. Finance and Stochastics,
3(3):251¨C273, 1999.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
