arXiv subjects

Muqiao Huang

Publications and source records attributed to Muqiao Huang.

5 recordsLinked to original sources

arXiv2026

Equilibrium in closed constant-function market maker economies

We study equilibria in a closed, fee-free constant-function market maker (CFMM) economy with two assets and two traders. An interior state is a unilateral no-trade equilibrium exactly when the CFMM marginal price equals both traders' marginal rates of substitution. For an interior initial state, individually rational unilateral equilibria are Pareto optimal relative to the fixed CFMM invariant. A weak representative agent is obtained at each fixed equilibrium by weighted sup-convolution, whereas a state-independent strong representative agent exists exactly when traders share a common homothetic preference. Every interior feasible state is reachable through finitely many valid trades, and alternating utility-maximizing trades converge to a Pareto optimal unilateral equilibrium. We also derive conditions under which trading order produces a first-mover advantage or disadvantage in the first round.

q-fin.TR↗

arXiv2026

Partial comonotonicity and distortion riskmetrics

We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing concepts of comonotonicity and single-point concentration. For two random variables, being comonotonic with a third one does not imply that they are comonotonic; instead, this defines an instance of partial comonotonicity. Any specific instance of partial comonotonicity uniquely characterizes a class of distortion riskmetrics through additivity under this dependence structure. An implication of this result is the characterization of the Expected Shortfall using single-point concentration.

q-fin.RM↗

arXiv2026

Lambda Expected Shortfall

The Lambda Value-at-Risk (Lambda-VaR) is a generalization of the Value-at-Risk (VaR), which has been actively studied in quantitative finance. Over the past two decades, the Expected Shortfall (ES) has become one of the most important risk measures alongside VaR because of its various desirable properties in the practice of optimization, risk management, and financial regulation. Analogously to the intimate relation between ES and VaR, we introduce the Lambda Expected Shortfall (Lambda-ES), as a generalization of ES and a counterpart to Lambda-VaR. Our definition of Lambda-ES has an explicit formula and many convenient properties, and we show that it is the smallest quasi-convex and law-invariant risk measure dominating Lambda-VaR under mild assumptions. We examine further properties of Lambda-ES, its dual representation, and related optimization problems.

q-fin.MF↗

arXiv2025

Coherent risk measures and uniform integrability

We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random variables, which is convenient in studying integrability, we work directly with random loses and gains, which have clear financial interpretation. We introduce a technical tool called the folding score of distortion risk measures. The analysis of the folding score allows us to convert some conditions on absolute values to those on gains and losses. As our main results, we obtain three sets of equivalent conditions for uniform integrability. In particular, a set is uniformly integrable if and only if one can find a coherent distortion risk measure that is bounded on the set, but not finite on $L^1$.

q-fin.RM↗

arXiv2024

A new characterization of second-order stochastic dominance

We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the resulting position generally less desirable for risk-averse agents. A similar characterization is also found for convex order and increasing convex order. The proof techniques for the main result are based on properties of Expected Shortfall, a family of risk measures that is popular in banking and insurance regulation. Applications in risk management and insurance are discussed.

q-fin.RM↗