In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory.

Spending on investments in integrative information systems (IIS) has considerably risen during the last few years due to a high need for linking various information systems. The demand for integrating the systems stems from developments like mergers and acquisitions and is typically satisfied in practice using Enterprise Application Integration solutions, Enterprise Resource Planning systems, Portals, or Data Warehouses. For the valuation of such an investment previous literature recommends the use of a real options analysis (ROA) since traditional capital budgeting methods such as the Net Present Value underestimate its value. Contrary, the ROA is able to conveniently account for managerial flexibility, represented by the possibility to implement follow-on opportunities, generated by the IIS. However, in practice ROA suffers from a lack of appliance mainly because of its complexity. This thesis precisely closes this gap and develops a simplified process model for a ROA by exactly tailoring the broad real options concept to the requirements of an investment valuation of IIS. For that, it reviews option pricing models from the financial world as well as previous research in the area of ROA and creates the desired model by conducting a ROA for four case studies in detail. The study reveals new findings concerning the question of how a decision-maker can apply the real options method and at the same time, when he/she is able to abandon a detailed ROA or a ROA at all. (author's abstract)

The thesis is focused on the options of quantifying credit risk by using the concept of the KMV model. The introduction outlines the basic approaches to measuring credit risk. In the following chapters is specified the nature of KMV model with the focus on its application in the Czech capital market. Self-calibration of the KMV model is made in this part. The analytical part related to the quantification of credit risk using the KMV model is implemented on selected companies which are traded on the Prague Stock Exchange. The results obtained are consequently confronted with the official rating degrees of agency Moody's.

Companiesissuing insurance cover, in return for insurance premiums, face the payments ofclaims occurring according to a loss distribution. Hence, capital must be heldby the companies so that they can guarantee the fulfilment of the claims ofeach line of insurance. The increased incidence of insurance insolvencymotivates the birth of new legislations as the European Solvency II Directive.Companies have to determine the required amount of capital and the optimalcapital allocation across the different lines of insurance in order to keep therisk of insolvency at an adequate level. The capital allocation problem may betreated in different ways, starting from the insurance company balance sheet.Here, the running process and efficiency of four methods are evaluated andcompared so as to point out the characteristics of each of the methods. TheValue-at-Risk technique is straightforward and can be easily generated for anyloss distribution. The insolvency put option principle is easily implementableand is sensitive to the degree of default. The capital asset pricing model isone of the oldest reliable methods and still provides very helpful intermediateresults. The Myers and Read marginal capital allocation approach encouragesdiversification and introduces the concept of default value. Applications ofthe four methods to some fictive and real insurance companies are provided. Thethesis further analyses the sensitivity of those methods to changes in the economiccontext and comments how insurance companies can anticipate those changes.

Black-Scholes選擇權定價模型是各種選擇定價的開山始祖，無論在理論或實務上均獲致許多的便利及好評，美中不足的是，這種既定模型下結構化參數的估計問題，在真實體系的結構訊息未知或是不明朗時，或是模式錯誤，亦或政治結構或金融環境不知時，該模型在實證資料的評價上會面臨價格偏誤的窘境。是故，許多的數值演算法（numerical algorithms）便因應而生，這些方法一則源於對此基本模型的修正，一則是屬於逼近的數值解。 評價選擇權的方法雖不一而足，然所有的這些理論或模型可分為二大類即模型驅動的理論（model-drive approach）及資料驅動的理論（data-driven approach）。前者是建構在許多重要的假設，當這些假設成立時，則選擇權的價格可用如Black-Scholes偏微分方程來表示，而後再用數值解法求算出，許多的數值方法即屬於此類的範疇；而資料驅動的理論（data-driven approach），其理論的特色是它的有效性（validity）不像前者是依其假設，職是之故，他在處理現實世界的財務資料時更顯見其具有極大的彈性。這些以計算智慧（computation intelligence）為主的財務計量方法，如人工神經網路（ANNs），遺傳演算法（GAs），遺傳規劃（GP）已在財務工程（financial engineering）領域上萌芽，並有日趨蓬勃的態勢，而將機器學習技術（machine learning techniques）應用在衍生性商品的定價，應是目前財務應用上最複雜及困難，亦是最富挑戰性的問題。 本文除了對現有文獻的整理評析外，在人工神經網路方面，除用於S&P 500的實證外，並用於台灣剛推行不久的認購構證評價之實證研究；而遺傳規劃在計算智慧發展的領域中，算是較年輕的一員，但發展卻相當的快速，雖目前在經濟及財務上已有一些文獻，但就目前所知的二篇文獻選擇權定價理論的文獻中，仍是試圖學習Black-Scholes選擇權定價模型，而本文則提出修正模型，使之成為完全以資料驅動的模型，應用於S&P 500實證，亦證實可行。最後，本文結合計算智慧中的遺傳演算法（ genetic algorithms）及數學上的加權殘差法（weight-residual method）來建構一條除二項式定價模型，人工神經網路定價模型，遺傳規劃定價模型等資料驅動模型之外的另一種具適應性學習能力的選擇權定價模式。 / The option pricing development rapid in recent years. However, the recent rapid development of theory and the application can be traced to the pathbreaking paper by Fischer Black and Myron Scholes(1973). In that pioneer paper, they provided the first explicit general equilibrium solution to the option pricing problem for simple calls and puts and formed a basis for the contingent claim asset pricing and many subsequent academic studies. Although the Black-Scholes option pricing model has enjoyed tremendous success both in practice and research, Nevertheless, it produce biased price estimates. So, many numerical algorithms have advanced to modify the basic model. I classified these traditional numerical algorithms and computational intelligence methods into two categories. Namely, the model-driven approach and the data-driven approach. The model-driven approach is built on several major assumptions. When these assumption hold, the option price usually can be described as a partial differential equation such as the Black-Scholes formula and can be solved numerically. Several numerical methods can be regarded as a member of this category. There are the Galerkin method, finite-difference method, Monte-Carlo method, etc. Another is the data-driven approach. The validity of this approach does not rests on the assumptions usually made for the model-driven one, and hence has a great flexibility in handling real world financial data. Artificial neural networks, genetic algorithms and genetic programming are a member of this approach. In my dissertation, I take a literature review about option pricing. I use artificial neural networks in S & P 500 index option and Taiwan stock call warrant pricing empirical study. On the other hand, genetic programming development rapid in recent three years, I modified the past model and contruct a data-driven genetic programming model. andThen, I usd it to S & P 500 index option empirical study. In the last, I combined genetic algorithms and weight-residual method to develop a option pricing model.