I develop a new mechanism for risk allocation and information speculation called a dynamic pari-mutuel market (DPM). A DPM acts as hybrid between a pari-mutuel market and a continuous double auction (CDA), inheriting some of the advantages of both. Like a pari-mutuel market, a DPM offers infinite buy-in liquidity and zero risk for the market institution; like a CDA, a DPM can continuously react to new information, dynamically incorporate information into prices, and allow traders to lock in gains or limit losses by selling prior to event resolution. The trader interface can be designed to mimic the familiar double auction format with bid-ask queues, though with an addition variable called the payoff per share. The DPM price function can be viewed as an automated market maker always offering to sell at some price, and moving the price appropriately according to demand. Since the mechanism is pari-mutuel (i.e., redistributive), it is guaranteed to pay out exactly the amount of money taken in. I explore a number of variations on the basic DPM, analyzing the properties of each, and solving in closed form for their respective price functions.

We develop a framework for trading in compound securities: financial instruments that pay off contingent on the outcomes of arbitrary statements in propositional logic. Buying or selling securities -- which can be thought of as betting on or against a particular future outcome -- allows agents both to hedge risk and to profit (in expectation) on subjective predictions. A compound securities market allows agents to place bets on arbitrary boolean combinations of events, enabling them to more closely achieve their optimal risk exposure, and enabling the market as a whole to more closely achieve the social optimum. The tradeoff for allowing such expressivity is in the complexity of the agents' and auctioneer's optimization problems.

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Recently, there has been an increase in the usage of centrally managed markets which are run by some form of pari-mutuel mechanism. A parimutuel mechanism is characterized by the ability to shield the market organizer from financial risk by paying the winners from the stakes of the losers. The recent introduction of new, modified pari-mutuel methods has spurred the growth of prediction markets as well as new financial derivative markets. Coinciding with this increased usage, there has been much work on the research front which has produced several mechanisms and a slew of interesting results. We will introduce a new pari-mutuel market-maker mechanism with many positive qualities including convexity, truthfulness and strong performance. Additionally, we will provide the first quantitative performance comparison of some of the existing pari-mutuel market-maker mechanisms. 1

The Federal Communications Commission uses an ascending bid auction called the Simultaneous Multi-round Auction (SMA) to assign spectrum for personal communication service licenses. Congress recently mandated that the SMA be evaluated to determine if it could be modified to allow "combinatorial" bids for packages of licenses. We review the theoretical background and prior experimental evidence relevant to the SMA procedures and their inherent defects which are driven largely by the presumption that values are cormnon or affiliated and that bidder identities must be revealed in real time. We present results from experiments to evaluate the SMA and some its more important rules, along with a comparative test of the SMA with a combinatorial auction specifically designed for the Federal Communications Commission by Charles River and Associates. We find that several of the SMA rules hinder efficiency and create a trade-offbetween efficiency and time to complete the auction. In addition, when license values are superadditive the combinatorial auction outperforms the SMA, but requires much more time to complete and is not robust with respect to boundary cases.

Abstract. We present a useful new mechanism that facilitates the atomic exchange of many large baskets of securities in a combinatorial exchange. Cryptography prevents information about the securities in the baskets from being exploited, enhancing trust. Our exchange offers institutions who wish to trade large positions a new alternative to existing methods of block trading: they can reduce transaction costs by taking advantage of other institutions ’ available liquidity, while third party liquidity providers guarantee execution—preserving their desired portfolio composition at all times. In our exchange, institutions submit encrypted orders which are crossed, leaving a “remainder”. The exchange proves facts about the portfolio risk of this remainder to third party liquidity providers without revealing the securities in the remainder, the knowledge of which could also be exploited. The third parties learn either (depending on the setting) the portfolio risk parameters of the remainder itself, or how their own portfolio risk would change if they were to incorporate the remainder into a portfolio they submit. In one setting, these third parties submit bids on the commission, and the winner supplies necessary liquidity for the entire exchange to clear. This guaranteed clearing, coupled with external price discovery from the primary markets for the securities, sidesteps difficult combinatorial optimization problems. This latter method of proving how taking on the remainder would change risk parameters of one’s own portfolio, without revealing the remainder’s contents or its own risk parameters, is a useful protocol of independent interest. 1

Combinatorial exchanges are trading mechanisms that allow agents to specify preferences over bundles of goods. When agents ’ preferences exhibit complementarity and/or substitutability, this additional expressiveness can lead to more efficient allocations than is possible using traditional exchanges. In the context of combinatorial exchanges, this paper examines arbitrage, a risk-free profit opportunity. We show that some combinatorial exchanges allow agents to perform arbitrage and thus extract a positive payment from the market while contributing nothing, something that is not possible in traditional exchanges. We analyze the extent to which arbitrage is possible and computationally feasible in combinatorial exchanges. We show that the surplus-maximizing combinatorial exchange with free disposal is resistant to arbitrage, but without free disposal arbitrage is possible. For volume-maximizing and liquidity-maximizing combinatorial exchanges, we show that arbitrage is sometimes possible and we propose an improved combinatorial exchange that achieves the same economic objective but eliminates a particularly undesirable form of arbitrage. We show that the computational complexity of detecting winning arbitraging bids is NP-complete and that the ability for an agent to submit arbitraging bids depends on the type of feedback in the exchange. We also show that a variant of combinatorial exchanges in which arbitrage is impossible becomes susceptible to arbitrage if certain side constraints are placed on the allocation or if an approximating clearing algorithm is used.

Recently, coinciding with and perhaps driving the increased popularity of prediction markets, several novel pari-mutuel mechanisms have been developed such as the logarithmic market scoring rule (LMSR), the cost-function formulation of market makers, utility-based markets, and the sequential convex pari-mutuel mechanism (SCPM). In this work, we present a convex optimization framework which unifies these seemingly unrelated models for centrally organizing contingent claims markets. The existing mechanisms can be expressed in our unified framework by varying the choice of a concave value function. We show that this framework is equivalent to a convex risk minimization model for the market maker. This facilitates a better understanding of the risk attitudes adopted by various mechanisms. The unified framework also leads to easy implementation since we can now find the cost function of a market maker in polynomial time by solving a simple convex optimization problem. In addition to unifying and explaining the existing mechanisms, we use the generalized framework to derive necessary and sufficient conditions for many desirable properties of a prediction market mechanism such as proper scoring, truthful bidding (in a myopic sense), efficient computation, controllable risk-measure, and guarantees on the worst-case loss. As a result, we develop the first proper, truthful, risk controlled, loss-bounded (in number of states) mechanism; none of the previously proposed mechanisms possessed all

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comparison of stock market mechanisms