Related papers: Classifying Financial Markets up to Isomorphism
We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal…
We define risk-free portfolios using three gauge invariant differential operators that require such portfolios to be insensitive to price changes, to be self-financing, and to produce a zero real return so there are no risk-free profits.…
This is a review about financial dependencies which merges efforts in econophysics and financial economics during the last few years. We focus on the most relevant contributions to the analysis of asset markets' dependencies, especially…
This paper characterizes the probability of a market failure defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through…
We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability…
In this paper we aim to study viability and completeness in finite markets. In order to do that, we characterize the set of equivalent martingale measures of two-period markets as convex combinations of a finite number of martingale…
Based on geometrical considerations, we propose a new oscillator for technical market analysis, the tube oscillator. This oscillator measures the trending behavior of a fixed market instrument based on its past history. It is shown in an…
This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and…
A generalized continuous economic model is proposed for random markets. In this model, agents interact by pairs and exchange their money in a random way. A parameter controls the effectiveness of the transactions between the agents. We show…
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,…
We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for…
In this review article we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions…
Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it…
The Mutual Fund Theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. It is established that: 1) Let N be the wealth process of…
In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the…
We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions we prove the existence of optimal strategies for investors who maximize their worst-case utility over a class of possible models. We…