scholarly journals Trajectory based market models with operational assumptions

2021 ◽  
Author(s):  
Andrew W. L. Fleck
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
A Priori ◽  
Mathematical Finance ◽  
Contingent Claim ◽  
Market Models ◽  
Market Prices ◽  
Sources Of Uncertainty ◽  
Price Movements ◽  
Different Sources

Mathematical finance makes use of stochastic processes to model sources of uncertainty in market prices. Such models have helped in the assessment of many financial situations. These approaches impose the stochastic process a priori which is then fitted to data. Hence, unchecked hypotheses can creep into the formalism and observable phenomena plays little role in building the model fundamentals. We attempt to reverse the procedure in order to include presumably more realistic price movements. Operational assumptions are used to construct a trajectory set relating discrete chart properties with investors' portfolio re-balancing preferences. By identifying features of these trajectories we can construct models that capture different sources of risk and use a geometric procedure to produce replication bounds for a contingent claim. Why a future unfolding chart fails to belong to the proposed trajectory set is testable. A preliminary risk-reward analysis based on this is also developed.

scholarly journals Trajectory based market models with operational assumptions

2021 ◽  
Author(s):  
Andrew W. L. Fleck
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
A Priori ◽  
Mathematical Finance ◽  
Contingent Claim ◽  
Market Models ◽  
Market Prices ◽  
Sources Of Uncertainty ◽  
Price Movements ◽  
Different Sources

Mathematical finance makes use of stochastic processes to model sources of uncertainty in market prices. Such models have helped in the assessment of many financial situations. These approaches impose the stochastic process a priori which is then fitted to data. Hence, unchecked hypotheses can creep into the formalism and observable phenomena plays little role in building the model fundamentals. We attempt to reverse the procedure in order to include presumably more realistic price movements. Operational assumptions are used to construct a trajectory set relating discrete chart properties with investors' portfolio re-balancing preferences. By identifying features of these trajectories we can construct models that capture different sources of risk and use a geometric procedure to produce replication bounds for a contingent claim. Why a future unfolding chart fails to belong to the proposed trajectory set is testable. A preliminary risk-reward analysis based on this is also developed.

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

scholarly journals A Double-indexed Functional Hill Process and Applications

2016 ◽  
Vol 8 (4) ◽  
pp. 144
Author(s):  
Modou Ngom ◽  
Gane Samb Lo
Keyword(s):  
Stochastic Process ◽  
Distribution Function ◽  
Asymptotic Behaviour ◽  
Stochastic Processes ◽  
Order Statistics ◽  
Finite Dimension ◽  
Domain Of Attraction ◽  
Extreme Value ◽  
Extreme Value Index

<div>Let $X_{1,n} \leq .... \leq X_{n,n}$ be the order statistics associated with a sample $X_{1}, ...., X_{n}$ whose pertaining distribution function (\textit{df}) is $F$. We are concerned with the functional asymptotic behaviour of the sequence of stochastic processes</div><div> </div><div>\begin{equation}<br />T_{n}(f,s)=\sum_{j=1}^{j=k}f(j)\left( \log X_{n-j+1,n}-\log<br />X_{n-j,n}\right)^{s} ,  \label{fme}<br />\end{equation}</div><div> </div><div>indexed by some classes $\mathcal{F}$ of functions $f:\mathbb{N}%^{\ast}\longmapsto \mathbb{R}_{+}$ and $s \in ]0,+\infty[$ and where $k=k(n)$ satisfies</div><div> </div><div>\begin{equation*}<br />1\leq k\leq n,k/n\rightarrow 0\text{ as }n\rightarrow \infty .<br />\end{equation*}</div><div> </div><div>We show that this is a stochastic process whose margins generate estimators of the extreme value index when $F$ is in the extreme domain of attraction. We focus in this paper on its finite-dimension asymptotic law and provide a class of new estimators of the extreme value index whose performances are compared to analogous ones. The results are next particularized for one explicit class $\mathcal{F}$.</div>

scholarly journals Combined electricity pricing model taking into account the “green tariff” and traditional factors

2021 ◽  
Vol 234 ◽  
pp. 00019
Author(s):  
Yuliia Halynska ◽  
Tetiana Bondar
Keyword(s):  
Methodological Approach ◽  
Electricity Pricing ◽  
End User ◽  
Combined Model ◽  
Pricing Policy ◽  
Economic Interests ◽  
Market Prices ◽  
Multiplier Effects ◽  
Alternative Sources ◽  
Different Sources

The article proposes a new optimization model of systemic relationships and effects in the formation of a pricing policy for electricity from combined sources of electricity, taking into account indicators of anthropogenic impact and non-renewable resources, socio-environmental and economic interests of society in the distribution of rental income. The model in the end result provides for the formation of a combined model of tariff setting in the energy sector, according to which electricity tariffs for the end user of the corresponding region will combine both market prices for energy generated from alternative sources and prices for energy generated from traditional sources. The authors improved the scientific and methodological approach to identify, formalize and quantify the multiplier effects that arise as a result of a combination of non-renewable and renewable sources of electricity. Also, the article improves the scientific and methodological approach to assessing the benefits of combining different sources of electricity and their advantages when forming a pricing policy within a single energy strategy.

scholarly journals Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem

2021 ◽  
Author(s):  
Jorma Jormakka ◽  
Sourangshu Ghosh
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Polynomial Time ◽  
Knapsack Problem ◽  
Generating Functions ◽  
General Theorem ◽  
Main Idea ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Linear Transform

The paper describes a method of solving some stochastic processes using generating functions. A general theorem of generating functions of a particular type is derived. A generating function of this type is applied to a stochastic process yielding polynomial time algorithms for certain partitions. The method is generalized to a stochastic process describing a rather general linear transform. Finally, the main idea of the method is used in deriving a theoretical polynomial time algorithm to the knapsack problem.

scholarly journals Markov Stochastic Processes in Biology and Mathematics -- the Same, and yet Different

2018 ◽  
Vol 14 (1) ◽  
pp. 7540-7559
Author(s):  
MI lOS lAWA SOKO
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Discrete Time ◽  
Stochastic Matrix ◽  
Random Number Generator ◽  
Point Of View ◽  
State Transitions ◽  
Similar Principle ◽  
Probabilistic Space ◽  
And Mathematics

Virtually every biological model utilising a random number generator is a Markov stochastic process. Numerical simulations of such processes are performed using stochastic or intensity matrices or kernels. Biologists, however, define stochastic processes in a slightly different way to how mathematicians typically do. A discrete-time discrete-value stochastic process may be defined by a function p : X0 × X → {f : Î¥ → [0, 1]}, where X is a set of states, X0 is a bounded subset of X, Î¥ is a subset of integers (here associated with discrete time), where the function p satisfies 0 < p(x, y)(t) < 1 and  EY p(x, y)(t) = 1. This definition generalizes a stochastic matrix. Although X0 is bounded, X may include every possible state and is often infinite. By interrupting the process whenever the state transitions into the X −X0 set, Markov stochastic processes defined this way may have non-quadratic stochastic matrices. Similar principle applies to intensity matrices, stochastic and intensity kernels resulting from considering many biological models as Markov stochastic processes. Class of such processes has important properties when considered from a point of view of theoretical mathematics. In particular, every process from this class may be simulated (hence they all exist in a physical sense) and has a well-defined probabilistic space associated with it.

On the modeling of linear system input stochastic processes with given accuracy and reliability

2018 ◽  
Vol 24 (2) ◽  
pp. 129-137
Author(s):  
Iryna Rozora ◽  
Mariia Lyzhechko
Keyword(s):  
Banach Space ◽  
Stochastic Process ◽  
Linear System ◽  
Stochastic Processes ◽  
Impulse Response Function ◽  
Output Process ◽  
Gaussian Stochastic Process ◽  
System Input ◽  
Time Invariant ◽  
Gaussian Stochastic Processes

AbstractThe paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions under which the constructed model approximates a Gaussian stochastic process with given accuracy and reliability in the Banach space{C([0,1])}, taking into account the response of the system. For this purpose, the methods and properties of square-Gaussian processes are used.

A Machine Learning-Based System for Predicting Service-Level Failures in Supply Chains

2021 ◽  
Author(s):  
Gabrielle Gauthier Melançon ◽  
Philippe Grangier ◽  
Eric Prescott-Gagnon ◽  
Emmanuel Sabourin ◽  
Louis-Martin Rousseau
Keyword(s):  
Machine Learning ◽  
Supply Chain ◽  
Service Level ◽  
Learning System ◽  
Safety Stock ◽  
Service Levels ◽  
Sources Of Uncertainty ◽  
Supply Chain Efficiency ◽  
Percentage Points ◽  
Different Sources

Despite advanced supply chain planning and execution systems, manufacturers and distributors tend to observe service levels below their targets, owing to different sources of uncertainty and risks. These risks, such as drastic changes in demand, machine failures, or systems not properly configured, can lead to planning or execution issues in the supply chain. It is too expensive to have planners continually track all situations at a granular level to ensure that no deviations or configuration problems occur. We present a machine learning system that predicts service-level failures a few weeks in advance and alerts the planners. The system includes a user interface that explains the alerts and helps to identify failure fixes. We conducted this research in cooperation with Michelin. Through experiments carried out over the course of four phases, we confirmed that machine learning can help predict service-level failures. In our last experiment, planners were able to use these predictions to make adjustments on tires for which failures were predicted, resulting in an improvement in the service level of 10 percentage points. Additionally, the system enabled planners to identify recurrent issues in their supply chain, such as safety-stock computation problems, impacting the overall supply chain efficiency. The proposed system showcases the importance of reducing the silos in supply chain management.

Criteria for the non-ergodicity of stochastic processes: application to the exponential back-off protocol

1987 ◽  
Vol 24 (02) ◽  
pp. 347-354 ◽  
Author(s):  
Guy Fayolle ◽  
Rudolph Iasnogorodski
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Stochastic Processes ◽  
State Space ◽  
Discrete Time ◽  
Random Variables ◽  
Countable State Space ◽  
Countable State ◽  
New Criteria

In this paper, we present some simple new criteria for the non-ergodicity of a stochastic process (Yn ), n ≧ 0 in discrete time, when either the upward or downward jumps are majorized by i.i.d. random variables. This situation is encountered in many practical situations, where the (Yn ) are functionals of some Markov chain with countable state space. An application to the exponential back-off protocol is described.

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