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### Strictly Proper Contract Functions Can Be Arbitrage-Free [article]

Eric Neyman, Tim Roughgarden
2021 arXiv   pre-print
We resolve this question positively, exhibiting a class of strictly proper arbitrage-free contract functions.  ...  These contract functions have two parts: one ensures that the total reward of a coalition of experts depends only on the average of their reports; the other ensures that changing this average report hurts  ...  Let Π be the contract function defined by Π i (P; j) = s quad (p i ; j) − (m − 1) 2 s quad (p −i ; j) + αp −i,j for each i, j. Then Π is strictly proper and arbitrage-free.  ...

### Strictly Proper Contract Functions Can Be Arbitrage-Free

Eric Neyman, Tim Roughgarden
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
We resolve this question positively, exhibiting a class of strictly proper arbitrage-free contract functions.  ...  These contract functions have two parts: one ensures that the total reward of a coalition of experts depends only on the average of their reports; the other ensures that changing this average report hurts  ...  Let Π be the contract function defined by Π i (P; j) = s quad (p i ; j) − (m − 1) 2 s quad (p −i ; j) + αp −i,j for each i, j. Then Π is strictly proper and arbitrage-free.  ...

### Preventing Arbitrage from Collusion When Eliciting Probabilities

Rupert Freeman, David M. Pennock, Dominik Peters, Bo Waggoner
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
Second, we discover strictly arbitrage-free mechanisms that satisfy an intermediate guarantee between weak and strict properness.  ...  First, we present a novel strictly proper mechanism that does not admit arbitrage provided that the reports of the agents are bounded away from 0 and 1, a common assumption in many settings.  ...  An Arbitrage-Free Rule Under Bounded Reports In this section we present a strictly proper contract function.  ...

### Strictly Proper Mechanisms with Cooperating Players [article]

SangIn Chun, Ross D. Shachter
2012 arXiv   pre-print
Traditional and competitive strictly proper scoring rules have been shown to incentivize players to provide truthful probabilistic forecasts.  ...  However, we show that when those players can cooperate, these mechanisms can instead discourage them from reporting what they really believe.  ...  Theorem 1 (Arbitrage with Binary E). Given binary E, any contract function for a strictly proper scoring rule admits arbitrage with identical reports.  ...

### Dual representation of superhedging costs in illiquid markets

Teemu Pennanen
2011 Mathematics and Financial Economics
Validity of the dual expressions is proved under new relaxed conditions related to the classical no-arbitrage condition.  ...  This paper studies superhedging of contingent claims in illiquid markets where trading costs may depend nonlinearly on the traded amounts and portfolios may be subject to constraints.  ...  Sufficient conditions for the closedness will be given in Section 4 where it is shown, in particular, that it holds in classical liquid market models that are free of "arbitrage".  ...

### Optimal investment and contingent claim valuation in illiquid markets

Teemu Pennanen
2014 Finance and Stochastics
Explicit consideration of swap contracts is essential in illiquid markets where the valuation of swaps cannot be reduced to the valuation of cumulative claims at maturity.  ...  This paper extends basic results on arbitrage bounds and attainable claims to illiquid markets and general swap contracts where both claims and premiums may have multiple payout dates.  ...  Indeed, Theorems 6 and 8 hold for any market model (S, D) arbitrage-free or not.  ...

### Viability and Arbitrage Under Knightian Uncertainty

Matteo Burzoni, Frank Riedel, H. Mete Soner
2017 Social Science Research Network
In a general framework, we discuss the absence of arbitrage, its relation to economic viability, and the existence of suitable nonlinear pricing expectations.  ...  In that case, one can take ˆ to be the zero contract and c * = 0.  ...  In the language of this paper, this property can be reformulated as: every relevant contract has a positive price.  ...

### SUPERHEDGING IN ILLIQUID MARKETS

Teemu Pennanen
2010 Mathematical Finance
We give alternative sufficient conditions that apply to market models with general convex cost functions and portfolio constraints.  ...  Such securities are common in practice where, due to illiquidity, wealth cannot be transferred quite freely in time.  ...  When C is algebraically closed, the finiteness of π(0) is necessary and sufficient for the superhedging cost π to be a proper convex function on M.  ...

### Perturbation analysis of sub/super hedging problems

Sergey Badikov, Mark H.A. Davis, Antoine Jacquier
2021 Mathematical Finance
We investigate the links between various no-arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein.  ...  No-arbitrage conditions, either in this abstract setting or in the case of a market consisting of European Call options, give rise to duality properties of infinite-dimensional sub-and super-hedging problems  ...  It can be shown that is continuous, strictly positive and linear as a simple corollary to Theorem 2.8.  ...

### On the range of admissible term-structures [article]

Areski Cousin
2014 arXiv   pre-print
can be derived for those quantities at the most liquid maturities.  ...  We then show how mean-reverting term structure models can be used as generators of admissible curves.  ...  The curve is arbitrage-free if P (t 0 , t) is a nonincreasing function of t.  ...

### A theory of pricing private data

Chao Li, Daniel Yang Li, Gerome Miklau, Dan Suciu
2017 Communications of the ACM
We identify essential properties of the price function and micropayments, and characterize valid solutions.  ...  The idea of monetizing private data can improve over the narrower view of hiding private data, since it empowers individuals to control their data through financial means.  ...  We prove that any arbitrage-free pricing function satisfies the following simple properties: Proposition 13. Let π be an arbitrage-free pricing function.  ...

### A Theory of Pricing Private Data

Chao Li, Daniel Yang Li, Gerome Miklau, Dan Suciu
2014 ACM Transactions on Database Systems
We identify essential properties of the price function and micropayments, and characterize valid solutions.  ...  The idea of monetizing private data can improve over the narrower view of hiding private data, since it empowers individuals to control their data through financial means.  ...  We prove that any arbitrage-free pricing function satisfies the following simple properties: Proposition 13. Let π be an arbitrage-free pricing function.  ...

### A theory of pricing private data

Chao Li, Daniel Yang Li, Gerome Miklau, Dan Suciu
2013 Proceedings of the 16th International Conference on Database Theory - ICDT '13
We identify essential properties of the price function and micro-payments, and characterize valid solutions.  ...  The idea of monetizing private data can improve over the narrower view of hiding private data, since it empowers individuals to control their data through financial means.  ...  We prove that any arbitrage-free pricing function satisfies the following simple properties: Proposition 13. Let π be an arbitrage-free pricing function.  ...

### Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II

Fabien Le Floc'h, Cornelis Oosterlee
2019 Risks
This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities.  ...  Finally, we consider a challenging example where convex spline interpolations lead to oscillations in the implied volatility and compare the spline collocation results with those obtained through arbitrage-free  ...  The mapping function only needs to be monotonic, and to conserve the first moment, in order for the collocation method to be arbitrage-free.  ...

### Cost function market makers for measurable spaces

Yiling Chen, Mike Ruberry, Jenn Wortman Vaughan
2013 Proceedings of the fourteenth ACM conference on Electronic commerce - EC '13
It differs from prior approaches in that it allows arbitrary market beliefs, not just those that admit density functions.  ...  Additionally, we show that scoring rules are derived from the same duality and share a close connection with cost functions for eliciting beliefs.  ...  Lemma 1 (Strictly Convex Functions of Absolutely Continuous Measures). Let ψ : R → R be a strictly convex function.  ...
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