01-18, 2022

本文是金融專業的paper代寫范例，題目是“Stochastic Modelling and Techniques in Financial Management（財務管理中的隨機模型和技術）”，精算師越來越多地使用“隨機建?！边@個術語。這意味著，對隨機模型最常見的解釋往往是考慮到未來結果的不確定性，一個非常復雜的計算引擎，包含大量的技術數學，必須運行幾百或幾千次。

**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.

考慮隨機過程{Xn, n = 0, 1, 2,…},數量有限或可數的可能狀態和一些已知的概率j,如果如果鏈目前狀態,然后移動到國家sj概率用j的一步,我在哪里j從狀態的概率是j。如果Xn =我,那么這個過程在時間n時處于狀態i。假設我們說，無論何時這個過程處于狀態i，它下一次處于狀態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隱馬爾可夫模型**

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.

隱馬爾可夫模型是一個雙重隨機過程，其中一個潛在的隨機過程是不可觀測的，這意味著狀態是隱藏的。這只能通過另一個產生一系列觀察結果的隨機過程來觀察。因此，如果S = {Sn, n= 1,2，…}為馬爾可夫過程，F = {Fk, k= 1,2，…}為S的函數，則S為通過F觀察到的隱馬爾可夫過程或隱馬爾可夫模式。

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確定性建模:專業服務的訂約**

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，財務模型是決策的關鍵因素，在整個衛生保健的預算編制和新項目規劃過程中經常建立。模型可以是確定性的，也可以是隨機的。確定性模型假定完全的可預測性，而隨機模型容納隨機性和概率，以反映未來輸入的不確定性。

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.

套利定價理論(APT)又稱套利定價模型(APM)，是將單因素CAPM推廣為多因素模型的一種方法。APT背后的理念是，由于生產、通貨膨脹、期限結構和其他經濟因素的意外變化，收益與預期值之間存在差異。在多因素模型中，假設資產的回報是用更多因素或指數的線性組合來解釋的。請注意，在CAPM中，資產的預期收益只是預期市場收益的線性函數。APT的發展基于有效市場的假設，見I.9。APT的技術實現使用了兩種流行的統計方法，回歸分析和因子分析。

**Techniques技術**

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.

基于馬爾可夫結構的數據處理技術。它考慮了一個給定的適當標記的樹結構已經在模擬過程中。此外，序列過程可以采用迭代細化的離散表示的基礎連續數據處理。前面提到的常用優化算法和軟件工具的主要優點是，它們易于使用，并且對于中等規模的問題都經過了良好的測試。

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

**Interpretation解釋**

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.

這個金融市場體系是為了促進互惠互利的跨期交易。金融市場通過組織各種金融證券的交易來促進這些交易。金融市場影響個人公司的財務生活和一個國家的經濟健康。融資是必不可少的，它有助于新業務的形成和現有業務的發展。金融趨勢還決定了全球經濟的狀況，因此央行可以制定適當的貨幣政策。

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.

關于認知偏差如何影響決策的全面討論超出了本文的范圍，但由于認識到它們的存在需要認識到并減輕它們，因此簡要地強調了三種常見的認知偏差。當對一項活動或項目的預估受到經驗和感知的影響時，錨點偏見會影響個人或組織的財務假設。支持介入放射設備投資的財務預測可能會被拒絕，因為在一個技術不那么復雜的時代，考慮到操作效率或優先考慮患者舒適度的經驗。固住過去的估值可能會導致醫院管理者放棄對新的放射治療套件更有利的預測，而選擇在財務上不太有利的手術套件，這僅僅是因為手術在過去產生了更大的利潤。

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