Friday, September 6, 2024

Simulating Stochastic Processes: A Mathematical Exploration of Markov Chains and Random Walks

 This paper presents a detailed exploration of simulation techniques in mathematics, focusing on the application of Markov Chains and Random Walks. Learn how these stochastic models are used to simulate complex processes in customer experience and stock market analysis.

Q1 Markov chain and Random Walk

Markov chain is a mathematical model involving unstructured circumstances happening with a particular time where the past influence the future using the present. Markov chain technique is utilized for modeling a series of activities or events. Markov Chain customer experience events are structured in such that task has series of events with different lengths (Brooks et al., 1998).  In other words, it comprise of a sequence of touch pint with the customer such as ads and emails. Technicality, the transition matrix from the technique has potentialities to function as quantitative metric of the Customer Relationship management (CRM) efficiency and to directly involve to the success of all the touch points.

 The Random Walk is a mathematical model used in the stock analysis. Random walk technique is used where the variables follow no discernible trend and pans out randomly.  The technique is widely used in the stock market. Its theory premise is on the assumption that random walking influence the evolving of the prices of securities in the stock market. Therefore, for the investors, the best approach is to invest in the market portfolio.

Q2. DES

 Discreet-event-simulation is a model that stimulates the behavior and the performance of the real-life process.  The approach is salient for increasing efficiency, speed and the performance (Bosilj et al., 2017).  For the system, DES not only analyzes the behavior of the system buy also conducts experiments with the adjustment of the system structure.

 Amongst the characteristics of the DES, it that is a technique for conducting experiment.  The attribute is vital for the monitoring and prediction of the behavior of investments in the stock market.  For businesses using the approach it is possible to predict the start and end of peak and off-peak season to facilitate sound investment. Also it facilitates devising approaches to mitigate complex problems. In other words, traders have the ability to predict the performance of the market during unprecedented times.

Q3. Semi-structured decisions

 Decision support framework is divided into three sub categories: unstructured, semi-structured and structured decision. Unstructured decision involves three decision phases (“intelligence, design and choice”) which are not structured, for example, sourcing for a company venue for end of year meeting. Structured decision involves phases that are follows a particular order, for example, a company selecting an appropriate investment partner. Finally, semi structured decisions involves combination of structured and unstructured problems and elements. For example, a company setting promotion budget for a new product.

 Semi-structured decision entails the following controls: Strategic planning, management control and operational control. Strategic planning is central for the business to longer range of objectives and policies such as production scheduling. For example the organization may decide to develop a policy that will require them to choose between sugar and biscuits to produce in the future.  The second factor is the managerial control that encompasses gathering of resources and prudently utilization to attain the goal of the company. For example, a semi-structured decisions on the acquisition of the technology to aid and enhance the process of the budget preparation. Lastly is the operational control factor that is casted on robustly performing the tasks. For example, the organization planning for the annual compensation of the employees based on the performance.

 

 

 

References

Bosilj Vukšić, V., Pejić Bach, M., & Tomičić-Pupek, K. (2017). Utilization of discrete event simulation in business processes management projects: a literature review. Journal of Information and Organizational Sciences, 41(2), 137-159.

Brooks, S. P. (1998). Markov Chain Monte Carlo Method and Its Application. Journal of the Royal Statistical Society. Series D (The Statistician), 47(1), 69–100. http://www.jstor.org/stable/2988428

 

 


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