9,951 research outputs found
A method for pricing American options using semi-infinite linear programming
We introduce a new approach for the numerical pricing of American options.
The main idea is to choose a finite number of suitable excessive functions
(randomly) and to find the smallest majorant of the gain function in the span
of these functions. The resulting problem is a linear semi-infinite programming
problem, that can be solved using standard algorithms. This leads to good upper
bounds for the original problem. For our algorithms no discretization of space
and time and no simulation is necessary. Furthermore it is applicable even for
high-dimensional problems. The algorithm provides an approximation of the value
not only for one starting point, but for the complete value function on the
continuation set, so that the optimal exercise region and e.g. the Greeks can
be calculated. We apply the algorithm to (one- and) multidimensional diffusions
and to L\'evy processes, and show it to be fast and accurate
Some numerical methods for solving stochastic impulse control in natural gas storage facilities
The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP
A Monte-Carlo study of meanders
We study the statistics of meanders, i.e. configurations of a road crossing a
river through "n" bridges, and possibly winding around the source, as a toy
model for compact folding of polymers. We introduce a Monte-Carlo method which
allows us to simulate large meanders up to n = 400. By performing large "n"
extrapolations, we give asymptotic estimates of the connectivity per bridge R =
3.5018(3), the configuration exponent gamma = 2.056(10), the winding exponent
nu = 0.518(2) and other quantities describing the shape of meanders.
Keywords : folding, meanders, Monte-Carlo, treeComment: 12 pages, revtex, 11 eps figure
A STOCHASTIC SIMULATION-BASED HYBRID INTERVAL FUZZY PROGRAMMING APPROACH FOR OPTIMIZING THE TREATMENT OF RECOVERED OILY WATER
In this paper, a stochastic simulation-based hybrid interval fuzzy programming (SHIFP) approach
is developed to aid the decision-making process by solving fuzzy linear optimization problems.
Fuzzy set theory, probability theory, and interval analysis are integrated to take into account the
effect of imprecise information, subjective judgment, and variable environmental conditions. A
case study related to oily water treatment during offshore oil spill clean-up operations is conducted
to demonstrate the applicability of the proposed approach. The results suggest that producing a
random sequence of triangular fuzzy numbers in a given interval is equivalent to a normal
distribution when using the centroid defuzzification method. It also shows that the defuzzified
optimal solutions follow the normal distribution and range from 3,000-3,700 tons, given the
budget constraint (CAD 110,000-150,000). The normality seems to be able to propagate
throughout the optimization process, yet this interesting finding deserves more in-depth study
and needs more rigorous mathematical proof to validate its applicability and feasibility. In
addition, the optimal decision variables can be categorized into several groups with different
probability such that decision makers can wisely allocate limited resources with higher
confidence in a short period of time. This study is expected to advise the industries and
authorities on how to distribute resources and maximize the treatment efficiency of oily
water in a short period of time, particularly in the context of harsh environments
A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding
Set-membership estimation is usually formulated in the context of set-valued
calculus and no probabilistic calculations are necessary. In this paper, we
show that set-membership estimation can be equivalently formulated in the
probabilistic setting by employing sets of probability measures. Inference in
set-membership estimation is thus carried out by computing expectations with
respect to the updated set of probability measures P as in the probabilistic
case. In particular, it is shown that inference can be performed by solving a
particular semi-infinite linear programming problem, which is a special case of
the truncated moment problem in which only the zero-th order moment is known
(i.e., the support). By writing the dual of the above semi-infinite linear
programming problem, it is shown that, if the nonlinearities in the measurement
and process equations are polynomial and if the bounding sets for initial
state, process and measurement noises are described by polynomial inequalities,
then an approximation of this semi-infinite linear programming problem can
efficiently be obtained by using the theory of sum-of-squares polynomial
optimization. We then derive a smart greedy procedure to compute a polytopic
outer-approximation of the true membership-set, by computing the minimum-volume
polytope that outer-bounds the set that includes all the means computed with
respect to P
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