Recent years have seen extensive studies on the pricing problem, as well as its many variances. They have found important applications in computational economics. Nowadays typical applications can be found in internet advertising, Google’s Auction for TV ads and many other resource allocation problems in electronic markets. In electronic markets, thousands of trading activities are processed in the internet or done automatically by computer programs. It is highly required that the trading mechanisms are efficient enough. In the thesis, we will study various pricing problems from different perspectives. The first problem we study is the design of auction mechanism when bidders are unit-demand. It can be applied in internet advertising. Thousand of advertisers bid for space in webpages to show their advertisements. We model the new problem and apply the General Second Price (GSP) mechanism to the problem. GSP is an efficient mechanism with linear time complexity. Moreover, we show that GSP has an envy-free equilibrium which can maximize the profit of advertisers. Auction mechanisms where bidders can bid for multiple items are also studied. A famous example of such auction is the Dutch flower auction. Such multi-unit auctions are widely studied these years. But budget constraints are not considered in many previous works. We study the scenario that each bidder has a budget on the money paid to the auctioneer and the valuation functions of bidders are non-linear. For the model, we design an adaptive clinching auction mechanism. The mechanism is proved to be incentive-compatible, which encourages bidders to reveal their true values, and Pareto-optimal, which ensures that no bidder can improve her utility without decreasing those of others. In some auctions, the items on sale are not available at the same time. For example, TV stations sell time-slots for advertisements on a daily basis. The advertisers are arriving and departing online and bidding for a set of timeslots. For the auction, we design a competitive mechanism which is truthful, i.e., all bidders have the incentive to submit their true private values to the auctioneer. Another important property the mechanism achieves is promptness, which makes sure that any advertiser that wins some time-slots could learn her payment immediately after winning these time-slots. In some pricing problems, upon the arrival of a new buyer, the seller needs to decide immediately whether he will sell his goods or not and what is the price. When buyers are unit-demand and each seller has b items on sale, the online pricing problem can be modelled by online weighted b-matching problem. For the problem, we show a randomized algorithm which achieves near-optimal competitive ratio. When buyers are not unit-demand, things are much more complicated. We consider a general model in which each buyer wants to buy a bundle of items and has a non-increasing valuation function for those items. We design a randomized algorithm which achieves low competitive ratio and derive a non-trivial lower bound on the competitive ratios. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.

We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.