Large agent and incomplete markets.

Most of the theoretical financial models assume that markets are complete and liquid. However, in practice, this is only approximately true and in many cases, different frictions and incompleteness have to be modeled to get accurate prices and better invest decisions. In this dissertation, we consider three this kind of cases. First, we model the optimal strategy in an incomplete market. We examine the optimal portfolio selection problem for a single agent who receives an unhedgeable endowment. The agent wishes to optimize his/her log-utility of terminal wealth. We rigorously prove that there exists a unique optimal portfolio strategy. We present a recursive computational algorithm which produces a sequence of portfolios converging to the optimal one. We present an intelligent initial portfolio which requires, numerically, about 25% fewer corrective steps in the algorithm than a random initial portfolio. Second, we consider the effect of stochastic parameters on the modeling of option prices. We use a jump-diffusion process for the underlying asset and the corresponding option pricing function. Our empirical analysis reveals that the negative jumps affect option price more significantly than other characteristics. However, due to the correlation between the parameters and the price, these characteristics affect hedging almost in similar magnitude. A test of a portfolio strategy and different hedging scenarios shows that hedging parameter uncertainty improves the performance of a delta hedge on average by 8% and increases the Sharpe Ratio by 21%. Third, we consider option hedging and pricing under a stochastic limit order book dynamics for the underlying asset. We model the underlying limit order book with a certain function and one risk factor. Then we calculate the corresponding close-from arbitrage free option pricing function. Our paper is related to large agent option pricing models that consider the option sellers price effect on the underlying asset. In the empirical analysis we fit our model to market price and compare it with existing large agent option pricing models. We should that our model fits the market prices better than the corresponding large agent models.PhDApplied SciencesFinanceIndustrial engineeringSocial SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125163/2/3186706.pd