48,770 research outputs found
Confidence level solutions for stochastic programming
We propose an alternative approach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable. The associated objective value is doubly random, since it depends on two outcomes: the event in the stochastic program and the randomized algorithm. We propose a solution concept in which the probability that the randomized algorithm produces a solution with an expected objective value departing from the optimal one by more than is small enough. We derive complexity bounds for this process. We show that by repeating the basic process on independent sample, one can significantly sharpen the complexity bounds
Single item stochastic lot sizing problem considering capital flow and business overdraft
This paper introduces capital flow to the single item stochastic lot sizing
problem. A retailer can leverage business overdraft to deal with unexpected
capital shortage, but needs to pay interest if its available balance goes below
zero. A stochastic dynamic programming model maximizing expected final capital
increment is formulated to solve the problem to optimality. We then investigate
the performance of four controlling policies: (), (), () and
(, , ); for these policies, we adopt simulation-genetic
algorithm to obtain approximate values of the controlling parameters. Finally,
a simulation-optimization heuristic is also employed to solve this problem.
Computational comparisons among these approaches show that policy and
policy provide performance close to that of optimal
solutions obtained by stochastic dynamic programming, while
simulation-optimization heuristic offers advantages in terms of computational
efficiency. Our numerical tests also show that capital availability as well as
business overdraft interest rate can substantially affect the retailer's
optimal lot sizing decisions.Comment: 18 pages, 3 figure
Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalities
Stochastic variational inequalities (SVI) model a large class of equilibrium
problems subject to data uncertainty, and are closely related to stochastic
optimization problems. The SVI solution is usually estimated by a solution to a
sample average approximation (SAA) problem. This paper considers the normal map
formulation of an SVI, and proposes a method to build asymptotically exact
confidence regions and confidence intervals for the solution of the normal map
formulation, based on the asymptotic distribution of SAA solutions. The
confidence regions are single ellipsoids with high probability. We also discuss
the computation of simultaneous and individual confidence intervals
On Designing Multicore-aware Simulators for Biological Systems
The stochastic simulation of biological systems is an increasingly popular
technique in bioinformatics. It often is an enlightening technique, which may
however result in being computational expensive. We discuss the main
opportunities to speed it up on multi-core platforms, which pose new challenges
for parallelisation techniques. These opportunities are developed in two
general families of solutions involving both the single simulation and a bulk
of independent simulations (either replicas of derived from parameter sweep).
Proposed solutions are tested on the parallelisation of the CWC simulator
(Calculus of Wrapped Compartments) that is carried out according to proposed
solutions by way of the FastFlow programming framework making possible fast
development and efficient execution on multi-cores.Comment: 19 pages + cover pag
Portfolio selection models: A review and new directions
Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalization of this approach leads to mean-risk models, in which a return distribution is characterized by the expected value of return (desired to be large) and a risk value (desired to be kept small). Portfolio choice is made by solving an optimization problem, in which the portfolio risk is minimized and a desired level of expected return is specified as a constraint. The need to penalize different undesirable aspects of the return distribution led to the proposal of alternative risk measures, notably those penalizing only the downside part (adverse) and not the upside (potential). The downside risk considerations constitute the basis of the Post Modern Portfolio Theory (PMPT). Examples of such risk measures are lower partial moments, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We revisit these risk measures and the resulting mean-risk models. We discuss alternative models for portfolio selection, their choice criteria and the evolution of MPT to PMPT which incorporates: utility maximization and stochastic dominance
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