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UBC Theses and Dissertations

Investment decisions in a dynamic environment Steele, Robert James


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.

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