114,823 research outputs found
Evolutionary multi-stage financial scenario tree generation
Multi-stage financial decision optimization under uncertainty depends on a
careful numerical approximation of the underlying stochastic process, which
describes the future returns of the selected assets or asset categories.
Various approaches towards an optimal generation of discrete-time,
discrete-state approximations (represented as scenario trees) have been
suggested in the literature. In this paper, a new evolutionary algorithm to
create scenario trees for multi-stage financial optimization models will be
presented. Numerical results and implementation details conclude the paper
A comparison of sample-based Stochastic Optimal Control methods
In this paper, we compare the performance of two scenario-based numerical
methods to solve stochastic optimal control problems: scenario trees and
particles. The problem consists in finding strategies to control a dynamical
system perturbed by exogenous noises so as to minimize some expected cost along
a discrete and finite time horizon. We introduce the Mean Squared Error (MSE)
which is the expected -distance between the strategy given by the
algorithm and the optimal strategy, as a performance indicator for the two
models. We study the behaviour of the MSE with respect to the number of
scenarios used for discretization. The first model, widely studied in the
Stochastic Programming community, consists in approximating the noise diffusion
using a scenario tree representation. On a numerical example, we observe that
the number of scenarios needed to obtain a given precision grows exponentially
with the time horizon. In that sense, our conclusion on scenario trees is
equivalent to the one in the work by Shapiro (2006) and has been widely noticed
by practitioners. However, in the second part, we show using the same example
that, by mixing Stochastic Programming and Dynamic Programming ideas, the
particle method described by Carpentier et al (2009) copes with this numerical
difficulty: the number of scenarios needed to obtain a given precision now does
not depend on the time horizon. Unfortunately, we also observe that serious
obstacles still arise from the system state space dimension
Risk-Averse Model Predictive Operation Control of Islanded Microgrids
In this paper we present a risk-averse model predictive control (MPC) scheme
for the operation of islanded microgrids with very high share of renewable
energy sources. The proposed scheme mitigates the effect of errors in the
determination of the probability distribution of renewable infeed and load.
This allows to use less complex and less accurate forecasting methods and to
formulate low-dimensional scenario-based optimisation problems which are
suitable for control applications. Additionally, the designer may trade
performance for safety by interpolating between the conventional stochastic and
worst-case MPC formulations. The presented risk-averse MPC problem is
formulated as a mixed-integer quadratically-constrained quadratic problem and
its favourable characteristics are demonstrated in a case study. This includes
a sensitivity analysis that illustrates the robustness to load and renewable
power prediction errors
Model-Based Security Testing
Security testing aims at validating software system requirements related to
security properties like confidentiality, integrity, authentication,
authorization, availability, and non-repudiation. Although security testing
techniques are available for many years, there has been little approaches that
allow for specification of test cases at a higher level of abstraction, for
enabling guidance on test identification and specification as well as for
automated test generation.
Model-based security testing (MBST) is a relatively new field and especially
dedicated to the systematic and efficient specification and documentation of
security test objectives, security test cases and test suites, as well as to
their automated or semi-automated generation. In particular, the combination of
security modelling and test generation approaches is still a challenge in
research and of high interest for industrial applications. MBST includes e.g.
security functional testing, model-based fuzzing, risk- and threat-oriented
testing, and the usage of security test patterns. This paper provides a survey
on MBST techniques and the related models as well as samples of new methods and
tools that are under development in the European ITEA2-project DIAMONDS.Comment: In Proceedings MBT 2012, arXiv:1202.582
Pricing and Hedging GLWB in the Heston and in the Black-Scholes with Stochastic Interest Rate Models
Valuing Guaranteed Lifelong Withdrawal Benefit (GLWB) has attracted
significant attention from both the academic field and real world financial
markets. As remarked by Forsyth and Vetzal the Black and Scholes framework
seems to be inappropriate for such long maturity products. They propose to use
a regime switching model. Alternatively, we propose here to use a stochastic
volatility model (Heston model) and a Black Scholes model with stochastic
interest rate (Hull White model). For this purpose we present four numerical
methods for pricing GLWB variables annuities: a hybrid tree-finite difference
method and a hybrid Monte Carlo method, an ADI finite difference scheme, and a
standard Monte Carlo method. These methods are used to determine the
no-arbitrage fee for the most popular versions of the GLWB contract, and to
calculate the Greeks used in hedging. Both constant withdrawal and optimal
withdrawal (including lapsation) strategies are considered. Numerical results
are presented which demonstrate the sensitivity of the no-arbitrage fee to
economic, contractual and longevity assumptions
A Consensus-ADMM Approach for Strategic Generation Investment in Electricity Markets
This paper addresses a multi-stage generation investment problem for a
strategic (price-maker) power producer in electricity markets. This problem is
exposed to different sources of uncertainty, including short-term operational
(e.g., rivals' offering strategies) and long-term macro (e.g., demand growth)
uncertainties. This problem is formulated as a stochastic bilevel optimization
problem, which eventually recasts as a large-scale stochastic mixed-integer
linear programming (MILP) problem with limited computational tractability. To
cope with computational issues, we propose a consensus version of alternating
direction method of multipliers (ADMM), which decomposes the original problem
by both short- and long-term scenarios. Although the convergence of ADMM to the
global solution cannot be generally guaranteed for MILP problems, we introduce
two bounds on the optimal solution, allowing for the evaluation of the solution
quality over iterations. Our numerical findings show that there is a trade-off
between computational time and solution quality
Planning for Decentralized Control of Multiple Robots Under Uncertainty
We describe a probabilistic framework for synthesizing control policies for
general multi-robot systems, given environment and sensor models and a cost
function. Decentralized, partially observable Markov decision processes
(Dec-POMDPs) are a general model of decision processes where a team of agents
must cooperate to optimize some objective (specified by a shared reward or cost
function) in the presence of uncertainty, but where communication limitations
mean that the agents cannot share their state, so execution must proceed in a
decentralized fashion. While Dec-POMDPs are typically intractable to solve for
real-world problems, recent research on the use of macro-actions in Dec-POMDPs
has significantly increased the size of problem that can be practically solved
as a Dec-POMDP. We describe this general model, and show how, in contrast to
most existing methods that are specialized to a particular problem class, it
can synthesize control policies that use whatever opportunities for
coordination are present in the problem, while balancing off uncertainty in
outcomes, sensor information, and information about other agents. We use three
variations on a warehouse task to show that a single planner of this type can
generate cooperative behavior using task allocation, direct communication, and
signaling, as appropriate
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