An optimization-based framework for automated market-making

Abstract

We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomial-time pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution's bounded budget.

Welfare Effects of Market Making in Continuous Double Auctions

“…Outside of microstructure, researchers have developed MM strategies for a variety of settings, including prediction markets (Hanson, 2007;Chen & Pennock, 2007;Abernethy, Chen, & Wortman Vaughan, 2011), dealer-mediated markets (Das, 2005;Jumadinova & Dasgupta, 2010), CDAs (Feng, Yu, & Stone, 2004), and environments where prices are generated exogenously (Abernethy & Kale, 2013). In this last category, Chakraborty and Kearns (2011) demonstrate the profitability of market making, given a mean-reverting price series.…”

Convex foundations for generalized MaxEnt models

“…Their regularity condition rules out all but Bregman divergences generated from log-convex generators. We recover their bijection and show that a much broader class of divergences correspond to GEFs via two key observations: 1) Like classical exponential families, GEFs have a "cumulant" C whose subdifferential contains the mean:We also show that every incomplete market with cost function C (see [2]) can be expressed as a complete market, where the prices are constrained to be a GEF with cumulant C. This provides an entirely new interpretation of prediction markets, relating their design back to the principle of maximum entropy. …”

“…We also show that every incomplete market with cost function C (see [2]) can be expressed as a complete market, where the prices are constrained to be a GEF with cumulant C. This provides an entirely new interpretation of prediction markets, relating their design back to the principle of maximum entropy.…”

Profit-charging market makers with bounded loss, vanishing bid/ask spreads, and unlimited market depth

“…Convex risk measures. Convex risk measures are the general class of market makers [Agrawal et al 2009;Othman and Sandholm 2011b] featured in much of the prediction market literature [Chen and Pennock 2007;Peters et al 2007;Agrawal et al 2009;Chen and Vaughan 2010;Othman and Sandholm 2010a;Abernethy et al 2011], including the most widely-used automated market maker in practice, the Logarithmic Market Scoring Rule (LMSR) [Hanson 2003[Hanson , 2007. These market makers can offer bounded worst-case loss and no marginal bid/ask spread.…”

“…(If we were to restrict our attention to path-indepedent market makers [Pennock and Sami 2007;Chen and Pennock 2007;Othman et al 2010;Abernethy et al 2011], worstcase loss would be much simpler to define, because those market makers operate only on their current payout vector, without regard to the past history of transactions. )…”