Related papers: Diversity and Arbitrage in a Regulatory Breakup Mo…
A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy…
We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market…
This paper studies the pricing and hedging of derivatives in frictionless and competitive, but incomplete jump-diffusion markets. A unique equivalent martingale measure (EMM) is obtained using filtration reduction to a fictitious complete…
We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure $\rho$. We first show that under mild assumptions, the set of optimal portfolios for a fixed return…
We consider a financial market in which traders potentially face restrictions in trading some of the available securities. Traders are heterogeneous with respect to their beliefs and risk profiles, and the market is assumed thin: traders…
We study models of regulatory breakup, in the spirit of Strong and Fouque [Ann. Finance 7 (2011) 349-374] but with a fluctuating number of companies. An important class of market models is based on systems of competing Brownian particles:…
A financial market is called "diverse" if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Ito-process model initiated by Samuelson (1965) we formulate this…
We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term…
Arbitrage can arise from the simultaneous purchase and sale of the same asset in different markets in order to profit from a difference in its price. This work systematically reviews arbitrage opportunities between Automated Market Makers…
Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price…
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market…
A financial market comprising of a certain number of distinct companies is considered, and the following statement is proved: either a specific agent will surely beat the whole market unconditionally in the long run, or (and this "or" is…
Along with the energy transition, the energy markets change their organization toward more decentralized and self-organized structures, striving for locally optimal profits. These tendencies may endanger the physical grid stability. One…
In this paper a finite discrete time market with an arbitrary state space and bid-ask spreads is considered. The notion of an equivalent bid-ask martingale measure (EBAMM) is introduced and the fundamental theorem of asset pricing is proved…
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…
The problem of allocating scarce items to individuals is an important practical question in market design. An increasingly popular set of mechanisms for this task uses the concept of market equilibrium: individuals report their preferences,…
Order matching systems form the backbone of modern equity exchanges, used by millions of investors daily. Thus, their operation is strictly controlled through numerous regulatory directives to ensure that markets are fair and transparent.…
We derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct…
In practice there are temporary arbitrage opportunities arising from the fact that prices for a given asset at different stock exchanges are not instantaneously the same. We will show that even in such an environment there exists a…
We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…