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The explicit consideration of certain types of uncertainty, in the analysis of investment opportunities, has become practical for the modern day decision maker. However, uncertainty analysis has generally been concerned with the probabilistic nature of future cash flows of investment opportunities. The uncertainty of cash flows, while extremely important in analysis, is by no means the only type of uncertainty which faces the decision maker. This thesis investigates another dimension of uncertainty by explicitly considering the possibility of better investment opportunities occurring in the future. A model is developed which approximates the interarrival time of investment opportunities by a sequence of independent and identically distributed random variables. The interarrival times are assumed to have a negative exponential probability density function, which corresponds to an Erlang family of probability density functions for the n th - order interarrival time. The present value, at the time the investment opportunity occurs, is assumed to be an element of a sequence of independent and identically distributed random variables. The distribution from which these random variables are drawn is assumed to be known. Using these independent families of random variables, a general model is developed. The above model is extended to take into account the effect of spending money in search of better investment opportunities. The amount spent on search is assumed to have an effect on the arrival rate of investment opportunities. Using the model described above, a number of interesting problems are analyzed. For a large class of problems the analysis determines the following: a) The expected value of continuing in search of better investment opportunities for a particular investment policy. b) The optimal investment policy which maximizes the expected value of continuing to search. c) The optimal level of search for a particular investment policy. d) The expected time until an acceptable investment, as defined by the investment policy, occurs. Numerical examples are formulated and numerical results for the above are determined. / Business, Sauder School of / Graduate

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Traditional methods for evaluating investments in state-of-the-art technology are sometimes found lacking in providing equitable recommendations for project selection. The major cause for this is the inability of these methods to handle adequately uncertainty and imprecision, and account for every aspect of the project, economic and non-economic, tangible and intangible. Fuzzy set theory provides an alternative to probability theory for handling uncertainty, while at the same time being able to handle imprecision. It also provides a means of closing the gap between the human thought process and the computer, by enabling the establishment of linguistic quantifiers to describe intangible attributes. Fuzzy set theory has been used successfully in other fields for aiding the decision-making process. The intention of this research has been the application of fuzzy set theory to aid investment decision making. The research has led to the development of a structured model, based on theoretical algorithms developed by Buckley and others. The model looks at a project from three different standpoints- economic, operational, and strategic. It provides recommendations by means of five different values for the project desirability, and results of two sensitivity analyses. The model is tested on a hypothetical case study. The end result is a model that can be used as a basis for promising future development of investment analysis models. / Master of Science / incomplete_metadata

Submitted in fulfillment of the requirements of the degree of Doctor of Technology: Business Administration, Durban University of Technology, Durban, South Africa, 2014. / The performance of portfolios of a fixed-rate asset and a risky asset of major companies in a South African market index the FTSE/JSE with strategies which rebalances fixed proportions of wealth in every rebalancing period is analysed in a long term. Recent findings in portfolio management theory by Dempster, Evstigneev and Schenk-Hoppé (2010, 2008, 2007, 2003) and by Browne (1988) note optimality of fixed-mix portfolios which assert fast exponential growth in stationary markets. A quantitative analysis is performed to analyse quantifiable measures in order to optimize the application of self-financing constant rebalanced portfolio strategies that contribute to the financial engineered prospects suggested by Dempster et al. (2010) for fixed-mix portfolios. The comparative performance of fixed-mix portfolios with a proxy strategy and without proxy strategy relative to a buy and hold strategy shows the superiority of fixed-mix portfolios in generic market conditions. The research extends the utilization of constant rebalanced self-financing portfolio investment strategies by assessing the market price of risk under the mean-variance model of Markowitz (1952). Effective implementation tactics of the strategy are examined by focusing on the market risk and the financial risk. The frequent reversals and trending of stochastic asset prices in the financial market are analysed to adjust the market price of risk by considering tradable financial securities to determine the financial proxy of de-trending. The proxy hypothesis which evaluates the stationary financial condition in a fixed-mix portfolio is validated by an option-based myopic strategy using a lookback straddle option. A myopic strategy is a strategy which considers a single period ahead, Fabozzi, Forcardi and Kolm (2006). The realised growth under a financial proxy is found to have a linear strategic asset allocation with a low degree of concavity relative to a buy and hold performance in the market risk of self-financing portfolio strategies. / D

This work contributes to the methodology of valuation of financial derivative contracts in an incomplete market. It focuses on a special type of incompleteness caused by the presence of a non-traded stochastic risk factor, affecting the value of the contract. The non-traded risk factor may only appear in the payoff of the contract or, in addition, may enter the dynamics of the traded asset. We consider both cases. We suggest a discrete time discrete space binomial model for the traded stock and the non-traded risk factor. We work in the utility maximization framework with dynamically changing agent's preferences. We present a discrete time multi-period analog of the forward and backward utility processes recently developed in continuous time. We use methods of stochastic control and provide the indifference valuation algorithm with both the forward and backward dynamic utilities. We compare the two approaches and provide conditions under which they assign the same value to the contract. We show that unlike the backward dynamic utility, the forward dynamic utility yields prices that do not depend on the end of the investment horizon. We pay attention to the choice of the equivalent martingale measure used for valuation (i.e., the minimal martingale measure and the minimal entropy measure for the forward and the backward utility processes correspondingly). We explicitly characterize both measures and give conditions under which they coincide. We extend our algorithm to the case of American and partial exercise contracts. We illustrate our work with numerical examples, showing that in an incomplete market, a call option on a non-traded risk factor may optimally be exercised early, and that it may be optimal to exercise only a fraction of the total number of contracts held, if partial exercise is allowed. In continuous time we extend the existing results to the case of American contracts with both the backward and the forward utilities. We emphasize the similarities between our discrete time valuation algorithm and the continuous time valuation. The two approaches use the same pricing measures, yield prices through nonlinear functionals of similar form, exhibit a similar relationship between the backward and forward prices, and a similar structure for the aggregate minimal entropy. We believe that our work makes a contribution by exposing the two above mentioned ways of dependence on the non-traded risk factor, and by providing a new dynamic indifference pricing algorithm that allows consistent valuation across different investment horizons.

This thesis presents the main results of my research in the field of computational finance and portfolios optimization. We focus on pricing Asian basket options and portfolio problems in the presence of inflation with stochastic interest rates.<p><p>In Chapter 2, we concentrate upon the derivation of bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework.We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151–168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3–33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55–57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51–90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1–52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity<p><p>In Chapter 3, we propose some moment matching pricing methods for European-style discrete arithmetic Asian basket options in a Black & Scholes framework. We generalize the approach of Curran M. (1994) [Valuing Asian and portfolio by conditioning on the geometric mean price”, Management science, 40, 1705-1711] and of Deelstra G. Liinev J. and Vanmaele M. (2004) [Pricing of arithmetic basket options by conditioning”, Insurance: Mathematics & Economics] in several ways. We create a framework that allows for a whole class of conditioning random variables which are normally distributed. We moment match not only with a lognormal random variable but also with a log-extended-skew-normal random variable. We also improve the bounds of Deelstra G. Diallo I. and Vanmaele M. (2008). [Bounds for Asian basket options”, Journal of Computational and Applied Mathematics, 218, 215-228]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and<p>time-to-maturity.<p><p>In Chapter 4, we use the stochastic dynamic programming approach in order to extend<p>Brennan and Xia’s unconstrained optimal portfolio strategies by investigating the case in which interest rates and inflation rates follow affine dynamics which combine the model of Cox et al. (1985) [A Theory of the Term Structure of Interest Rates, Econometrica, 53(2), 385-408] and the model of Vasicek (1977) [An equilibrium characterization of the term structure, Journal of Financial Economics, 5, 177-188]. We first derive the nominal price of a zero coupon bond by using the evolution PDE which can be solved by reducing the problem to the solution of three ordinary differential equations (ODE). To solve the corresponding control problems we apply a verification theorem without the usual Lipschitz assumption given in Korn R. and Kraft H.(2001)[A Stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40(4), 1250-1269] or Kraft(2004)[Optimal Portfolio with Stochastic Interest Rates and Defaultable Assets, Springer, Berlin].<p><p><p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished