Investment strategy with consumption in risky markets, avoiding unlimited profits.
problem Optimal investment with consumption in risky markets.
method Semimartingale model, utility stochastic field, NUPBR assumptions.
result Key conclusions of utility maximization theory hold under NUPBR.
This paper completes the analysis of Choulli et al. Non-Arbitrage up to Random Horizons and after Honest Times for Semimartingale Models and contains two principal contributions. The first contribution consists in providing and analysing many practical examples of market models that admit classical arbitrages while the…
Study arbitrage and utility in insider markets, proving criteria and strategies.
problem Arbitrage opportunities and market viability in insider markets.
method Criteria for No Unbounded Profits with Bounded Risk, optimal arbitrage strategies, utility maximization proofs.
result Characterization of optimal strategies and duality results for utility maximization.
Determines conditions for arbitrage in complex financial markets.
problem Identifying markets without arbitrage opportunities.
method Derives deterministic criteria for equivalent martingale measures.
result Constructs financial markets with specific risk conditions.
In a general semimartingale financial model, we study the stability of the No Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with Bounded Risk) condition under initial and under progressive filtration enlargements. In both cases, we provide a simple and general condition which is sufficient to…
The paper sets criteria for no arbitrage in complex financial models.
problem Determining conditions for the absence of arbitrage in financial markets.
method Established deterministic conditions for no arbitrage, NUPBR, and NFLVR in diffusion market models.
result Provided criteria in terms of scale function and speed measure.
We solve optimal consumption in a market with bounded risk.
problem Optimal consumption in a semimartingale market with bounded risk.
method Use supermartingale deflators to prove strong duality.
result Strong duality and complete characterisation of optimal consumption.
In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the same optimal strategy and u…
Study arbitrage theory without numéraire, generalizing NUPBR.
problem Arbitrage theory in markets without numéraire.
method Disintegration of probability space into crash times.
result Generalization of NUPBR to no unbounded profits with bounded risk.
We show that \emph{No unbounded profit with bounded risk} (NUPBR) implies \emph{predictable uniform tightness} (P-UT), a boundedness property in the Emery topology which has been introduced by C. Stricker \cite{S:85}. Combining this insight with well known results from J. Mémin and L. Słominski \cite{MS:91} leads to a …
Study no-arbitrage conditions in 1D diffusion markets with interest rates.
problem Determining no-arbitrage conditions in 1D diffusion markets with interest rates.
method Established deterministic criteria for no-arbitrage notions in terms of scale function and speed measure.
result Revealed various effects, e.g., NIP not excluded by reflecting boundaries.
We study the existence of the numeraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numeraire portfolio generates a wealth process, with respect to which the relative wealth processes of all other portfolios are supermartingales. Necessary and sufficient c…
Unified models for asset prices with transaction costs and infinite variation strategies.
problem Models with transaction costs and infinite variation strategies.
method Unified models using semimartingale price systems.
result Existence of a semimartingale price system consistent with transaction costs.
This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which is also known in the literature as the first kind of non-arbitrage. For this non-arbitrage notion, we ob…
Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.
problem Maximizing lifetime utility from wealth over an infinite horizon.
method Develops a duality theory using deflators and supermartingale properties, extending previous work.
result Establishes a strong duality theorem for infinite horizon utility maximization under minimal no-arbitrage assumptions.
This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of Aksamit/Choulli/Deng/Jeanblanc [1] in which the authors studied similar topics for the case of stopping…
This paper extends NUPBR concept for semimartingales with thin predictable sets.
problem Impact of random stopping times on NUPBR in semimartingale models.
method Progressive enlargement with random time, explicit construction of local martingale deflator.
result NUPBR property is affected by arbitrary random stopping times and honest times.
We develop a new bound for estimating CVaR from samples of an unbounded random variable.
problem Estimating CVaR from i.i.d. samples of an unbounded random variable.
method Derive a one-sided concentration bound for a CVaR estimator.
result A novel concentration bound for CVaR estimation.
Modeling gas fee competition in decentralized exchanges to optimize arbitrage profits.
problem Gas fees and transaction ordering in decentralized exchanges create arbitrage opportunities.
method Developed a first equilibrium model of gas fee competition between two arbitrageurs under three transaction reversion settings.
result Mixed equilibria exist, and their characteristics depend on inventory risk and transaction settings.
The paper shows how to find shadow prices for portfolio optimization with transaction costs in fractional Brownian motion models.
problem Finding shadow prices for portfolio optimization under transaction costs in models driven by fractional Brownian motion.
method Deriving shadow prices for exponential fractional Brownian motion under the condition of 'two way crossing' instead of requiring the process to be a semimartingale.
result Existence of shadow prices for exponential fractional Brownian motion and all utility functions defined on the positive half-line with reasonable asymptotic elasticity.
New method decomposes profits and losses continuously, avoiding discrete reporting issues.
problem Analyzing profits and losses at discrete dates ignores detailed paths.
method Constructs a large class of continuous-time decompositions using extended Itô's formula.
result Identifies a preferred decomposition from exactness, symmetry, and normalization axioms.
New bounds for general unbounded loss functions, optimizing for various estimators.
problem Excess risk bounds for general unbounded loss functions, including log loss and squared loss.
method Optimized bounds for η-generalized Bayesian, MDL, and empirical risk minimization estimators, using v-GRIP and witness conditions. result Achieves ildeO(1/n) rates for certain loss functions under favorable v and small model complexity. This paper proposes two approaches that quantify the exact relationship among the viability, the absence of arbitrage, and/or the existence of the numéraire portfolio under minimal assumptions and for general continuous-time market models. Precisely, our first and principal contribution proves the equivalence among the…
Paper provides uniform deviation bounds for unbounded loss functions, improving k-Means clustering bounds.
problem Uniform deviation bounds for unbounded loss functions, specifically k-Means clustering.
method Novel framework to obtain uniform deviation bounds for unbounded loss functions.
result Improved bounds for k-Means clustering under weak assumptions, achieving $\mathcal{O}\left(m^{-\frac12}
ight)$ rate.
Study analyzes smart contract adoption under bounded risk, showing stable adoption but fragile financial outcomes.
problem Understanding smart contract adoption in derivative markets under risk constraints.
method Structural theory linked with simulation and real-world validation.
result Adoption intensity is stable but profitability and service outcomes are sensitive to volatility.
New aggregation strategy handles unbounded losses with regret bounds.
problem Online optimization with unbounded loss functions.
method Follow The Regularized Leader (FTRL) with φ-divergence.
result Worst regret bound for unbounded losses with alternative divergences.
Two new algorithms improve performance in adversarial bandits with unbounded losses.
problem Adversarial Multi-Armed Bandits with unbounded losses.
method Developed UMAB-NN and UMAB-G for non-negative and general unbounded losses respectively.
result UMAB-NN achieves the first adaptive and scale-free regret bound for non-negative unbounded losses.
This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.
Study resolves duality gap in optimal consumption with random income termination.
problem Optimal consumption in a market with randomly terminating income.
method Established rigorous duality theory using supermartingale deflators.
result Closed duality gap and characterized optimal wealth process.
New algorithms optimize risk-aware selection in uncertain rewards.
problem Balancing expected reward and risk in uncertain, potentially heavy-tailed rewards.
method Distribution oblivious algorithms that consider CVaR, not bound on moments/tails.
result Provable upper bounds on incorrect identification probability.
Theoretical limits on verifying self-improving systems without risking unbounded utility.
problem Formalizing and proving the limits of safety verification for self-improving systems.
method Developed dual conditions and used Holder's inequality, NP counting method, and Lipschitz bounds to establish impossibility and ceiling results.
result A classifier-based safety gate cannot simultaneously permit unbounded beneficial self-modification and bounded cumulative risk.
Improved bounds for unbounded losses using transductive priors.
problem Sequential regression and classification with unbounded losses.
method Exponential weights algorithm with transductive priors.
result Statistical bounds independent of design vectors and optimal solution norm.
New PAC-Bayes training method improves model generalization for unbounded loss.
problem Improving generalization of complex models under unbounded loss.
method Established new PAC-Bayes bound for unbounded loss, jointly training prior and posterior.
result Outperforms existing PAC-Bayes training algorithms and matches ERM accuracy.
Study utility maximization in financial markets with bounded and unbounded payoffs.
problem Utility maximization in financial markets with constraints and unbounded payoffs.
method Combines quadratic backward stochastic differential equations and convex duality.
result Established utility indifference valuation, regime switching, and consumption-investment problems in unbounded markets.
The paper examines the tilted empirical risk's generalization and robustness under negative tilt.
problem The generalization error of machine learning algorithms under negative tilt.
method Uniform and information-theoretic bounds on the tilted generalization error under negative tilt.
result The tilted empirical risk's generalization error has a convergence rate of \(O(n^{-ε/(1+ε)})\).
Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.
problem Optimal risk in bounded distributions for constrained least squares.
method Comparison of least squares and non-linear predictors.
result Non-linear predictors can achieve optimal risk O(d/n) in bounded distributions. Optimizes Iron Condor portfolios for better risk and profit management.
problem Transient value process of Iron Condor portfolios not well studied.
method Formulated as a stochastic optimal control problem, using bounded martingale assumption.
result Optimal stopping time aligns with expiration for submartingale value process.
CREDIT learns to master pair trading with risk-aware RL, outperforming existing methods.
problem Challenges in applying RL to pair trading due to temporal correlations and risk considerations.
method Risk-aware recurrent reinforcement learning (RL) with bidirectional GRU and temporal attention.
result CREDIT achieves significant profit in pair trading over five years of U.S. stock data.
Paper extends chaining technique for empirical risk minimization bounds.
problem Empirical risk minimization with unbounded noise and estimates.
method Chaining technique applied to random design settings, proving excess risk bounds.
result Proves upper bounds for empirical risk minimization with sub-Gaussian or subexponential noise.
Study uncovers CDS anomalies leading to arbitrage profits.
problem Identifying arbitrage opportunities in CDS term structures.
method Derive No-arbitrage conditions for CDS term structures, analyze extensive dataset.
result Presented 2,416 pairs of anomalous CDS contracts.
Diversification improves profits for heavy-tailed investments.
problem Investment portfolios of Pareto-distributed returns.
method Stochastic dominance and majorization order.
result Diversification increases first-order stochastic dominance for heavy-tailed returns.
This paper develops a new dual risk model where profits and costs vary with wealth.
problem Traditional dual risk models assume constant costs and Poisson profits; this paper introduces variable costs and profits.
method Develops a state-dependent dual risk model with variable arrival rates of profits and costs.
result Ruin probabilities are derived in closed-form.
Proposes a new method to rank risky investments based on Omega measure.
problem Evaluating and ranking risky investment projects.
method Introduces an investment certainty equivalence approach and uses the Omega measure.
result Proposed method ranks projects differently from conventional risk-adjusted discount rate (RADR) approach.
Paper tackles robust deep learning from weakly dependent data with unbounded loss and input.
problem Tackles robust deep learning from weakly dependent data with unbounded loss and input.
method Establishes non-asymptotic bounds for expected excess risk under strong mixing and ψ-weak dependence assumptions. result Derives a relationship between bounds and r, and shows convergence rate close to i.i.d. results for r=∞. Paper establishes bounds for RNN-TPPs, showing four-layer networks can achieve vanishing errors.
problem Understanding theoretical limits of RNN-TPPs.
method Characterized RNN complexity, constructed neural approximations, applied truncation technique.
result Four-layer RNN-TPPs can achieve vanishing generalization errors.
This paper examines if CTE risk measure aligns with profit-maximizing risk capital allocations.
problem Whether CTE risk measure aligns with profit-maximizing risk capital allocations.
method Exhaustive probabilistic model settings analysis.
result CTE risk measure may align with profit-maximizing risk capital allocations under certain conditions.
We introduce a quantitative approach to comparative statics that allows to bound the maximum effect of an exogenous parameter change on a system's equilibrium. The motivation for this approach is a well known paradox in multimarket Cournot competition, where a positive price shock on a monopoly market may actually redu…
SMP estimator improves density and logistic regression under misspecification.
problem Improper estimator for optimal excess risk in misspecified models.
method SMP minimizes a new excess risk bound for statistical learning.
result SMP achieves optimal excess risk of O((d+B2R2)/n) for logistic regression.