Mathematics Commons^™

Options Portfolio Optimization And Hedging Of Exotic Options Written On Mini S&P 500 Index In An Illiquid Market With Conditional Value At Risk (Cvar), Benyanee Kosapong

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis investigates the derivatives for portfolio optimization. Risk measures such as Mean Variance (MV), Value-at-Risk (VaR), and Conditional Value-at-Risk (CVaR) are minimized. However, we focus primarily on CVaR because it is a coherent and convex risk measure. We adopt the method of Rockafellar and Uryasev (Journal of Risk 2, 3 (2000)), which minimizes CVaR for shares and convert this method to use with options written on the S&P500 Mini Index. The distribution is known and the index values are simulated by using the VG distribution, over CVaR constraints. In particular, the approach can be used for minimizing the CVaR …

Numerical Solutions For One– And Two–Dimensional Shallow Water Equations Based On Finite Integration Method With Chebyshev Expansion, Lalita Apisornpanich

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Mass Ratio Variance Majority Cleansing And Minority Oversampling Technique For Class Imbalanced, Piboon Polvimoltham

Chulalongkorn University Theses and Dissertations (Chula ETD)

A sampling method is one of the basic methods to deal with an imbalance problem appearing in machine learning. A dataset having an imbalance problem has a noticeably skewed distribution among different classes. There are three types of sampling techniques to solve this problem by balancing class distributions, undersampling technique, over-sampling technique, and combined sampling technique. In this research, the mass ratio variance scores of each data point of the same class are computed and used to remove noise from a majority class and synthesise instances from a minority class. The results of this proposed sampling technique improve recall over …

Identifying The Most Distinctive Characteristics Of A Good Solution For Non-Euclidean Cvrp Using Statistical Learning Model, Piyabut Inbunsong

Chulalongkorn University Theses and Dissertations (Chula ETD)

A capacitated vehicle routing problem (CVRP) is a well-known NP-hard combinatorial optimization. Therefore, heuristics are the common methods used to search for a good solution. The algorithms will perform better if characteristics of good solutions of the problem are known. There was a research study in the characteristics of Euclidean CVRP solutions and the knowledge was later applied in a metaheuristic. That study becomes our motivation to study the characteristics of non-Euclidean CVRP solutions. To that end, we considered the solutions of non-Euclidean CVRP in the new Euclidean space with the same or higher dimensions using multi-dimensional scaling in which …

Stochastic Control Model With Carrying Capacity Of Population Management Policy For Squirrels In Durian Orchards, Sasiwimol Auepong

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, the problem that squirrels ruin durian, which is an economic important fruit in Thailand, is considered. We seek for a strategy on squirrel elimination under the consideration that squirrels are not alien species in Thailand and also orchard ecosystem. The problem is solved through a stochastic control model. The population dynamics of squirrels is constructed as a controlled stochastic differential equation with carrying capacity, since we consider the squirrel population in a confined orchard. A performance index indicating the total benefit of a given squirrel elimination strategy is provided. The index comprises the countermeasure cost, resources loss, …

Finite Integration Method Using Chebyshev Expansion For Solving Heat Equation With Non-Local Boundary Conditions, Thanakorn Prasansri

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Numerical Algorithm For Heat Equation With Moving Boundary Using Finite Integration Method With Chebyshev Polynomial Expansion, Warunya Wong-U-Ra

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Eigenvalues Of Unitary Cayley Graph Of Matrix Algebras And Its Subconstituents, Jitsupat Rattanakangwanwong

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

The Cardinality Of The Permutations On A Set With N Non-Fixed Points, Jukkrid Nuntasri

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study relationships between |Sn(A)| and |seqn1-1(A)| as well as |seqn(A)| for infinite sets A, where Sn(A) is the set of permutations of A with n non-fixed points and seqn(A) and seqn1-1(A) are the set of sequences and the set of one-to-one sequences of elements of A with length n, respectively, where n is a natural number greater than 1. With the Axiom of Choice (AC), |Sn(A)|, |seqn1-1(A)|, and |seqn(A)| are equal for all infinite sets A. Among our results, we show, in the Zermelo-Fraenkel set theory (ZF), that |Sn(A)|<=|seqn1-1(A)| for any infinite set A under some weak form of AC and the assumption cannot be removed. In the other direction, we show that |seqn1-1(A)|<=|Sn+1(A)| for any infinite set A and the subscript n+1 cannot be reduced to n. Moreover, we also show that "|Sn(A)|<=|Sn+1(A)| for any infinite set A" is not provable in ZF.

Threshold Numbers Of Some Complete Multipartite Graphs And Their Complements, Thanaporn Sumalroj

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Amm Problem #12279, Brad Isaacson

Publications and Research

No abstract provided.

Lasso: Listing All Subset Sums Obediently For Evaluating Unbounded Subset Sums, Christopher N. Burgoyne, Travis J. Wheeler

Graduate Student Theses, Dissertations, & Professional Papers

In this study we present a novel algorithm, LASSO, for solving the unbounded and bounded subset sum problem. The LASSO algorithm was designed to solve the unbounded SSP quickly and to return all subsets summing to a target sum. As speed was the highest priority, we benchmarked the run time performance of LASSO against implementations of some common approaches to the bounded SSP, as well as the only comparable implementation for solving the unbounded SSP that we could find. In solving the bounded SSP, our algorithm had a significantly faster run time than the competing algorithms when the target sum …

New Development Of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, And Neutrosophic Plithogenic Optimizations, Florentin Smarandache, Yanhui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

This collective book presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.

Introduction To Superhyperalgebra And Neutrosophic Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we recall our concepts of n th-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m, n)- SuperHyperStructures).

Soft Set Product Extended To Hypersoft Set And Indetermsoft Set Product Extended To Indetermhypersoft Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we define the Soft Set Product as a product of many soft sets and afterwards we extend it to the HyperSoft Set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft Set. We also present several applications of the Soft Set Product to Fuzzy (and fuzzy-extensions) Soft Set Product and to IndetermSoft Set and IndetermHyperSoft Set.

The Reciprocal Of The Butterfly Theorem, Ion Patrascu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Linguistic Matrices, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. Most of the properties enjoyed by real and complex matrices are satisfied by these linguistic matrices. However, we see when we try to define operations on linguistic matrices that they behave in different ways. The possible operations defined on linguistic matrices are only the maximum and minimum. Further, we have different identities for min and max operations on these matrices for linguistic variable and its associated linguistic words.

Linguistic Functions, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, the authors have proved the analogues of the Bolzano Weierstrass theorem for the linguistic version. Several concepts in the case of linguistic continuum are very distinct from the natural classical real continuum. Categorically, we have three linguistic variables: one leading to a continuum, some finite and orderable set, and some not orderable. We define a linguistic plane associated with linguistic variables and give graphs associated with linguistic functions.

Linguistic Graphs And Their Applications, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The authors define the notion of directed linguistic graphs and linguistic-weighted graphs.

The second chapter discusses all types of linguistic graphs, linguistic dyads, linguistic triads, linguistic wheels, complete linguistic graphs, connected linguistic graphs, disconnected linguistic graphs, and linguistic components of the graphs. Further we define the notion of linguistic subgraphs of a linguistic graph. The third chapter also introduces the notion of Linguistic Cognitive Maps (LCMs) analogous to Fuzzy Cognitive maps (FCMs). We also propose Linguistic relational Maps, which are analogous to Fuzzy Relational Maps. These models find applications in problems whose data is unsupervised, but the values are linguistic.

Linguistic Geometry And Its Applications, W. B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The authors venture to define the notion of linguistic geometry in this book.

It is pertinent to keep on the record that linguistic geometry differs from the classical geometry.

Many fundamental concepts and notions of classical geometry are not valid or extendable in the case of linguistic geometry.

We discuss in dept the linguistic variables, graphs and geometry essential for social information networks.

And then develop the new notion of linguistic geometry and its related properties.

The concept of linguistic social information geometric networks is also developed.