01-18, 2022

本文是金融专业的Essay范例，题目是“Stochastic Modelling and Techniques in Financial Management（财务管理中的随机模型和技术）”，精算师越来越多地使用“随机建模”这个术语。这意味着，对随机模型最常见的解释往往是考虑到未来结果的不确定性，一个非常复杂的计算引擎，包含大量的技术数学，必须运行几百或几千次。

**Aim目的**

It is actuaries are increasingly using the term ‘stochastic modeling’. It means the most common interpretations of a stochastic model tends to be something that allows for uncertainty of future outcome, a very complicated calculation engine with lots of technical math’s involved something that must be run several hundred or thousand times.

Individuals and corporate are facing the problem in day-to-day life related to maximize the profits. They can either spend it immediately, or save it, or partially spend and partially save. In either of the possibilities, they must decide how to do that process. In the case of saving, they prorogue their immediate consume in favor of investment and also most of the individuals now-a-days participated in some type of retirement plan, either through their previous employer or in a self-business plan. The reason is that they want to get best financial security for them after retirement of their service. For this reason, most of the senior citizens and companies are invested huge money in the stock market. Changes of share prices on every day make it more volatile and difficult to predict the future price. When purchasing a stock, it does not guarantee anything in return. Thus, it makes stocks risky in investment, but investors can get high profit in return. When investors are taking wrong decision in choosing the counters, it may end up in capital loss. The behavior of stock market returns has been deeply discussed over some years. Stock market prediction is the art of trying to evaluate the future value of a company stock or other financial instrument traded on a financial exchange. There is no single method can accurately predict changes in the stock market every day. So, there are many stochastic models introduced many papers in predicting share prices and they are birth and death processes, random walk models, Markov chain, hidden Markov model (HMM) and Brownian motion model. In this paper, we discussed about the role of application perspective discussions on stochastic models in the field of finance.

**Methods方法**

Markov Chain

Consider a stochastic process {Xn, n=0, 1, 2, …} that takes on a finite or countable numbers of possible states with some known probabilities Pij, If the chain is currently in state si, then it moves to state sj at the step with a probability denoted by pij, where Pij is the probability of moving from state i to j. If Xn =i, then the process is said to be in state i at time n. Suppose we say that whenever the process is in state i, there is a fixed probability Pi j that it will next be in state j.

考虑随机过程{Xn, n = 0, 1, 2,…},数量有限或可数的可能状态和一些已知的概率j,如果如果链目前状态,然后移动到国家sj概率用j的一步,我在哪里j从状态的概率是j。如果Xn =我,那么这个过程在时间n时处于状态i。假设我们说，无论何时这个过程处于状态i，它下一次处于状态j的概率是固定的。

Suppose say that,

P{Xn+1 = j/Xn = i, Xn-1= in-1, …, X1 = i1, X0 = i0} = Pij For all states i0, i1,…,in-1, i, j and all n ≥ 0. Such type of stochastic process is known as a Markov chain.

Markov Chain is a time-indexed random process with the Markov property. Having the Markov property that means it gives the present state, the future states are independent of the past state, i.e. that for all t, the process [X(t + s)-X(t)|s ≥ 0] has the same distribution as the process [X(s) | 0 ≤ s ≤ t]

**Hidden Markov Model隐马尔可夫模型**

An HMM is a doubly stochastic process in which an underlying stochastic process is unobservable, which means that the state is hidden. This can only be observed through another stochastic process that produces a sequence of observations. Thus, if S = {Sn, n=1, 2,...} is a Markov process and F = {Fk , k=1, 2, …} is a Function of S, then S is a hidden Markov process or hidden Markov mode that is observed through F.

隐马尔可夫模型是一个双重随机过程，其中一个潜在的随机过程是不可观测的，这意味着状态是隐藏的。这只能通过另一个产生一系列观察结果的随机过程来观察。因此，如果S = {Sn, n= 1,2，…}为马尔可夫过程，F = {Fk, k= 1,2，…}为S的函数，则S为通过F观察到的隐马尔可夫过程或隐马尔可夫模式。

Modeling to Forecast the Future

Decisions are made based upon judgments that are influenced by analysis and instincts. Key to analysis is the use of historical and current performance characteristics as a basis for forecasting future performance, understanding that the future is difficult to predict. Consequently, the future might best be viewed in relation to statistically informed probabilities.

**Deterministic Modeling: Contracting for Professional Services确定性建模:专业服务的订约**

It is important in financial models that they are a critical element for decision making and are routinely created in the process of budgeting as well as new project planning throughout health care. Models can be deterministic or stochastic. Deterministic models assume perfect predictability, whereas stochastic models accommodate randomness and probabilities to reflect uncertainties of future inputs.

重要的是，财务模型是决策的关键因素，在整个卫生保健的预算编制和新项目规划过程中经常建立。模型可以是确定性的，也可以是随机的。确定性模型假定完全的可预测性，而随机模型容纳随机性和概率，以反映未来输入的不确定性。

From the above set of values, we observed that the probability of decrease to decrease, decrease to increase, increase to decrease and increase to increase values having same probability in 7th and subsequence days. From this empirical evidence, Markov chain is more useful and powerful to predict next day values; it is not reliable for subsequent days. In my observation all the above mentioned three types of Stochastic models were partially supported to prediction of the stock market, even some of the authors were strongly agree with the stock market prediction is not reliable to the investors. Some of the authors said that, their prediction method was more reliable for short term investors only. The above empirical result also shows that the Markov chain analysis is powerful tool for predict next day value only, which is not useful for lateral days.

**Analysis分析**

Use of the Arbitrage Pricing Theory, (APT) also known as Arbitrage Pricing Model, APM, serves as a generalization of the single factor CAPM to a multifactor model. The idea behind the APT is that the returns vary from their expected values due to unanticipated changes in production, inflation, term structure, and other economic factors. In the multifactor model it is supposed that the return on an asset is explained in terms of a linear combination of more factors or indexes. Note that in CAPM, the expected return on an asset is a linear function of the expected market return only. The development of APT is based on the assumptions of an efficient market, see I.9. A technical realization of APT uses two popular statistical methods, regression analysis and factor analysis.

套利定价理论(APT)又称套利定价模型(APM)，是将单因素CAPM推广为多因素模型的一种方法。APT背后的理念是，由于生产、通货膨胀、期限结构和其他经济因素的意外变化，收益与预期值之间存在差异。在多因素模型中，假设资产的回报是用更多因素或指数的线性组合来解释的。请注意，在CAPM中，资产的预期收益只是预期市场收益的线性函数。APT的发展基于有效市场的假设，见I.9。APT的技术实现使用了两种流行的统计方法，回归分析和因子分析。

**Techniques技术**

The techniques based on the Markov structure of data. It takes into account a given suitably labelled tree structure already in the course of simulation. Moreover, the sequential procedure can be adopted for an iterative refinement of the discrete representation of the underlying continuous data process. The main advantage of the aforementioned common optimization algorithms and software tools is that they are easy to use and well-tested for mid-size problems.

基于马尔可夫结构的数据处理技术。它考虑了一个给定的适当标记的树结构已经在模拟过程中。此外，序列过程可以采用迭代细化的离散表示的基础连续数据处理。前面提到的常用优化算法和软件工具的主要优点是，它们易于使用，并且对于中等规模的问题都经过了良好的测试。

However, the main disadvantage is that they are inefficient for large-scale stochastic programs as they do not utilize their special structure.

**Interpretation解释**

This system of financial markets is to facilitate mutually beneficial inter temporal exchanges. Financial markets promote these exchanges by organizing trading in a variety of financial securities. The financial market influences personal corporate financial lives and the economic health of a country. Finance is the essential, which helps in the formation of new businesses and to grow the current business. Financial trends also define the state of the economy on a global level, so central banks can plan appropriate monetary policies.

这个金融市场体系是为了促进互惠互利的跨期交易。金融市场通过组织各种金融证券的交易来促进这些交易。金融市场影响个人公司的财务生活和一个国家的经济健康。融资是必不可少的，它有助于新业务的形成和现有业务的发展。金融趋势还决定了全球经济的状况，因此央行可以制定适当的货币政策。

Conclusion

The behaviour of stock market returns is a common issue to the theory and practice of asset pricing, asset allocation, and risk management. There are various techniques implemented for the prediction of stock market. In this study we see that a complete theoretical survey of all the stock market prediction techniques are used for the different types of stochastic models that are given. Cognitive Biases in decision Making even with robust historical data, logical financial projections, and well-considered strategy, decisions can be shortcut by cognitive biases and heuristics, influencing the perception of risk.

A comprehensive discussion of how cognitive biases affect decision-making is beyond the scope of this article, but because an awareness of their existence is needed to recognize and mitigate them, three common cognitive biases are highlighted in brief. When a preconceived valuation for an activity or project is influenced by experiences and perceptions, anchor bias can colour an individual’s or an organization’s financial assumptions. Financial forecasts supporting an investment in interventional radiology facilities may be rejected based upon experiences during an era with less sophisticated technology, consideration for operational efficiency, or prioritized patient comfort. Anchoring to past valuations may lead a hospital administrator to reject a more favourable forecast for a new radiology procedure suite in favour of a less financially favourable surgery suite, simply because surgery has generated larger profits in the past.

关于认知偏差如何影响决策的全面讨论超出了本文的范围，但由于认识到它们的存在需要认识到并减轻它们，因此简要地强调了三种常见的认知偏差。当对一项活动或项目的预估受到经验和感知的影响时，锚点偏见会影响个人或组织的财务假设。支持介入放射设备投资的财务预测可能会被拒绝，因为在一个技术不那么复杂的时代，考虑到操作效率或优先考虑患者舒适度的经验。固住过去的估值可能会导致医院管理者放弃对新的放射治疗套件更有利的预测，而选择在财务上不太有利的手术套件，这仅仅是因为手术在过去产生了更大的利润。

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