arXiv subjects

Ted Theodosopoulos

Publications and source records attributed to Ted Theodosopoulos.

17 recordsLinked to original sources

arXiv2025

Topological Obstructions to Shared Priors

Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on the full space? This formulation of the consistency problem for conditional probabilities is significant in Bayesian epistemology and probabilistic reasoning, as it describes the conditions under which a collection of agents can reach agreement by sharing information. We derive a necessary and sufficient condition under which joint compatibility is equivalent to pairwise compatibility. This condition is stated in terms of the cohomology of a simplicial complex constructed from the given probability measures, exposing a novel application of algebraic topology to Bayesian reasoning.

math.PR↗

arXiv2015

Hierarchical Economic Agents and their Interactions

We present a new type of spin market model, populated by hierarchical agents, represented as configurations of sites and arcs in an evolving network. We describe two analytic techniques for investigating the asymptotic behavior of this model: one based on the spectral theory of Markov chains and another exploiting contingent submartingales to construct a deterministic cellular automaton that approximates the stochastic dynamics. Our study of this system documents a phase transition between a sub-critical and a super-critical regime based on the values of a coupling constant that modulates the tradeoff between local majority and global minority forces. In conclusion, we offer a speculative socioeconomic interpretation of the resulting distributional properties of the system.

math.PR↗

arXiv2013

On Agents and Equilibria

This essay discusses the advantages of a probabilistic agent-based approach to questions in theoretical economics, from the nature of economic agents, to the nature of the equilibria supported by their interactions. One idea we propose is that "agents" are meta-individual, hierarchically structured objects, that include as irreducible components groupings of different dimensions. We also explore the effects of non-ergodicity, by constructing a simple stochastic model for the contingent nature of economic interactions.

q-fin.GN↗

arXiv2006

Periodic attractors of random truncator maps

This paper introduces the \textit{truncator} map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure. A stochastic model is constructed on these endomorphisms, which leads to the classification of the distribution of periodic orbits for random truncator maps. This framework is applied to investigate the periodic transitions of Bornholdt's spin market model.

math.PR↗

arXiv2006

Imbalance attractors for a strategic model of market microstructure

In this paper we extend the series of our studies on the properties of an interacting particle model for market microstructure. In our earlier work we defined a Markov process on the majority opinion of the agents, obtained the transition probabilities and analyzed the martingale properties of the ensuing wealth process. Here we relax the assumption on the choices of individual agents by allowing mixed strategies, offering opportunities for the agents to gain intermediate submartingale exposure for their individual wealth processes. We develop a novel two-dimensional spin system to model the critical regions of the wealth process as a reflection of the agents' behaviors. We exhibit strategic conflicts between individual market participants and the market as a whole, and identify a new source of uncertainty arising from `reinforced expectations'.

math.PR↗

arXiv2006

Hybrid dynamics for currency modeling

We present a simple hybrid dynamical model as a tool to investigate behavioral strategies based on trend following. The multiplicative symbolic dynamics are generated using a lognormal diffusion model for the at-the-money implied volatility term structure. Thus, are model exploits information from derivative markets to obtain qualititative properties of the return distribution for the underlier. We apply our model to the JPY-USD exchange rate and the corresponding 1mo., 3mo., 6mo. and 1yr. implied volatilities. Our results indicate that the modulation of autoregressive trend following using derivative-based signals significantly improves the fit to the distribution of times between successive sign flips in the underlier time series.

math.PR↗

arXiv2005

Robustness and Evolvability of the B Cell Mutator Mechanism

We present a model that considers the maturation of the antibody population following primary antigen presentation as a global optimization problem. The trade-off that emerges from our model describes the balance between the safety of mutations that lead to local improvements in affinity and the necessity of the system to undergo global reconfigurations in the antibody's shape in order to achieve its goals, in this example of fast-paced evolution. The parameter p which quantifies this trade-off appears to be itself both robust and evolvable. This parallels the rapidity and consistency of the optimization operating during the biologic response. In this paper, we explore the robust qualities and evolvability of this tunable control parameter, p.

q-bio.QM↗

arXiv2005

Study on optimal timing of mark-to-market for contingent credit risk control

Over-the-counter derivatives have contributed significantly to the effectiveness and efficiency of the international financial system but also entail significant counterparty credit risk. Collateralization is one of the most important and widespread credit risk mitigation techniques used in derivatives transactions. However, the relevant decisions are often made in an ad-hoc manner, without reference to an analytical framework. Very little academic research has addressed the quantitative analysis of collateralization for contingent credit risk control. The issue of mark-to-market timing becomes important for reducing credit exposure of illiquid and long term derivative contracts due to the difficulty and cost of marking to market. the goal of this research is to propose a framework for minimizing the potential credit exposure of collateralized derivative transactions by optimizing mark-to-market timing.

math.PR↗

arXiv2005

A Reversion of the Chernoff Bound

This paper describes the construction of a lower bound for the tails of general random variables, using solely knowledge of their moment generating function. The tilting procedure used allows for the construction of lower bounds that are tighter and more broadly applicable than existing tail approximations.

math.PR↗

arXiv2005

Uncertainty relations in models of market microstructure

This paper presents a new interacting particle system and uses it as a spin model for financial market microstructure. The asymptotic analysis of this stochastic process exhibits a lower bound to the contemporaneous measurement of price and trading volume under the invariant measure in the `frozen' phase of the supercritical regime.

math.PR↗

arXiv2005

Properties of the wealth process in a market microstructure model

In this short paper we define the wealth process in a spin model for market microstructure, for individual agents and in aggregate. The agents in our model try to balance their desire to belong to the local majority (herding behavior), defined over random network neighborhoods, and the occasional advantage of belonging to the global minority (contrarian trading). We arrive at a classification of the martingale properties of this wealth process and use it to determine the strategic stability of the agents' interactions. Our goal is to add a behavioral interpretation to this stochastic agent-based model for market fluctuations.

math.PR↗

arXiv2005

Properties of a renewal process approximation for a spin market model

In this short note we investigate the natur of the phase transitions in a spin market model as a function of the interaction strength between local and global effects. We find that the stochastic dynamics of this stylized market model exhibit a periodicity whose dependence on the coupling constant in the Ising-like Hamiltonian is robust to changes in the temperature and the size of the market.

math.PR↗

arXiv2005

Statistical properties of the phase transitions in a spin model for market microstructure

Increased day-trading activity and the subsequent jump in intraday volatility and trading volume fluctuations has raised considerable interest in models for financial market microstructure. We investigate the random transitions between two phases of an agent-based spin market model on a random network. The objective of the agents is to balance their desire to belong to the global minority and simultaneously to the local majority. We show that transitions between the "ordered" and "disordered" phases follow a Poisson process with a rate that is a monotonically decreasing function of the network connectivity.

math.PR↗

arXiv2004

Short-term equity dynamics and endogenous market fluctuations

We present a model that investigates the spontaneous emergence of randomness in equity market microstructure. The phase space analysis of our model exposes an endogenous source of fluctuation in price and volume. We formulate a control problem for maximizing price regularity and stability while minimizing entanglement with the market, representing the NYSE specialists' affirmative obligation to maintain `fair and orderly markets'.

math.PR↗

arXiv2004

Some Remarks on the Optimal Level of Randomization in Global Optimization

For a class of stochastic restart algorithms we address the effect of a nonzero level of randomization in maximizing the convergence rate for general energy landscapes. The resulting characterization of the optimal level of randomization is investigated computationally for random as well as parametric families of rugged energy landscapes.

math.OC↗

arXiv2004

Evolution at the Edge of Chaos: A Paradigm for the Maturation of the Humoral Immune Response

We study the maturation of the antibody population following primary antigen presentation as a global optimization problem. Emphasis is placed on the trade-off between the safety of mutations that lead to local improvements to the antibody's affinity and the necessity of eventual mutations that result in global reconfigurations in the antibody's shape. The model described herein gives evidence of the underlying optimization process from which the rapidity and consistency of the biologic response could be derived.

q-bio.QM↗

arXiv2004

A computational study of the statistical mechanics of antibody-antigen conformations

We describe the representation of the chemical affinity between the antigen-combining site of the immunoglobulin molecule and the antigen molecule as the probability of the two molecules existing in a bound state. Our model is based on the identification of shape attractors in the configuration space for the joint antibody / antigen combining site sequence. We parameterize configuration space in terms of Ramachandran angles. The shape attractors allow us to construct a Markov chain whose steady state distribution gives rise to the desired attachment probability. As a result we are able to delineate the enthalpic, entropic and kinetic components of affinity and study their interactions.

q-bio.QM↗