Browsing by Subject "Prices--Mathematical models"
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Item Agents' agreement and partial equilibrium pricing in incomplete markets(2008-12) Anthropelos, Michail, 1980-; Žitković, GordanWe consider two risk-averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with non-traded random endowments, we provide necessary and sufficient conditions for the negotiation to be successful, i.e., for the trade to occur. We, also, study the asymptotic case where the size of the claim is small compared to the random endowments and give a full characterization in this case. We, then, study a partial-equilibrium problem for a bundle of divisible claims and establish its existence and uniqueness. A number of technical results on conditional indifference prices are provided. Finally, we generalize the notion of partial-equilibrium pricing in the case where the agents' risk preferences are modelled by convex capital requirements.Item Essays on pricing and portfolio choice in incomplete markets(2008-12) Zhou, Ti, 1981-; Zariphopoulou, Thaleia, 1962-This dissertation is a contribution to the pricing and portfolio choice theory in incomplete markets. It consists of three self-contained but interlinked essays. In the first essay, we present a utility-based methodology for the valuation and the risk management of mortgage-backed securities subject to totally unpredictable prepayment risk. Incompleteness stems from its embedded pre-payment option which affects the security's cash flow pattern. The prepayment time is constructed via deterministic or stochastic hazard rate. The relevant indifference price consists of a linear term, corresponding to the remaining outstanding balance, and a nonlinear one that incorporates the investor's risk aversion and the interest payments generated by the mortgage contract. The indifference valuation approach is also extended to the case of homogeneous mortgage pools. In the second essay, using forward optimality criteria, we analyze a portfolio choice problem when the local risk tolerance is time-dependent and asymptotically linear in wealth. This class corresponds to a dynamic extension of the traditional (static) risk tolerances associated with the power, logarithmic and exponential utilities. We provide explicit solutions for the optimal investment strategies and wealth processes in an incomplete non-Markovian market with asset prices modelled as Ito processes. The methodology allows for measuring the investment performance in terms of a benchmark and alter-native market views. In the last essay, we extend the forward investment performance approach to study the optimal portfolio choice problem in an incomplete market driven by jump processes. The asset price is modelled by a one-dimensional Lévy-Itô process. We prove the existence of a forward performance process by restricting the local risk tolerance functions to be time-independent and linear in wealth. This yields only three types of performance measurement criteria, namely, exponential, power and logarithmic. The optimal portfolios are constructed via stochastic feedback controls under these criteria.Item Integrating commodity markets in the procurement policies for different supply chain structures(2007) Goel, Ankur, 1976-; Gutierrez, Genaro J.This research develops a mathematical model of procurement for commodities which integrates the arbitrage free pricing models for commodities in Finance with the traditional inventory models of Operations Management. In essence, we develop a model that uses market determined information on spot and futures prices to ascertain the optimal procurement strategy. This research is an attempt to understand how firms should adapt their operating policies in presence of fluctuating commodity prices. In this research we seek to understand how the term structure of futures prices at a commodity market can be used in the formulation of procurement and distribution policies of supply chains under centralized decision making. The difference between spot and futures prices play an important role in the determination of the actual cost of holding a commodity; the cost of holding a unit of a tradable commodity is a random variable whose values are determined by the stochastic evolution of prices at the commodity market, and it is exogenously imposed on the firm. The benefits derived from storing a unit of the commodity, on the other hand, are endogenous to each firm and depends on its operational characteristics. Our research objective is to understand how the internal operational decisions of the firm should be modified as a function of the spot and futures prices observed in the market, in order to achieve an optimal balance between cost and benefits of holding an inventory. We model prices with a stochastic process that allows no risk-free arbitrage opportunities, and in this setting, we characterize optimal procurement and distribution policies for various supply chain structures. In addition, we explore the value of using two factor price model over one-factor price model on procurement costs. Our results suggest that there are substantial cost savings in inventory related costs on incorporating spot and futures price information in the procurement model. Furthermore, two-factor model yields higher cost savings than using a single factor model to forecast prices. Distribution of commodities requires the understanding of price dynamics on the commodity markets as well as the issues related to supply chains. This dissertation is an attempt to contribute to the understanding of this area of research.Item Three essays on the interface of computer science, economics and information systems(2007) Hidvégi, Zoltán Tibor, 1970-; Whinston, Andrew B.This thesis looks at three aspects related to the design of E-commerce systems, online auctions and distributed grid computing systems. We show how formal verification techniques from computer science can be applied to ensure correctness of system design and implementation at the code level. Through e-ticket sales example, we demonstrate that model checking can locate subtle but critical flaws that traditional control and auditing methods (e.g., penetration testing, analytical procedure) most likely miss. Auditors should understand formal verification methods, enforce engineering to use them to create designs with less of a chance of failure, and even practice formal verification themselves in order to offer credible control and assistance for critical e-systems. Next, we study why many online auctions offer fixed buy prices to understand why sellers and auctioneers voluntarily limit the surplus they can get from an auction. We show when either the seller of the dibbers are risk-averse, a properly chosen fixed permanent buy-price can increase the social surplus and does not decrease the expected utility of the sellers and bidders, and we characterize the unique equilibrium strategies of uniformly risk-averse buyers in a buy-price auction. In the final chapter we look at the design of a distributed grid-computing system. We show how code-instrumentation can be used to generate a witness of program execution, and show how this witness can be used to audit the work of self-interested grid agents. Using a trusted intermediary between grid providers and customers, the audit allows payment to be contingent on the successful audit results, and it creates a verified reputation history of grid providers. We show that enabling the free trade of reputations provides economic incentives to agents to perform the computations assigned, and it induces increasing effort levels as the agents' reputation increases. We show that in such a reputation market only high-type agents would have incentive to purchase a high reputation, and only low-type agents would use low reputations, thus a market works as a natural signaling mechanism about the agents' type.