Trading strategies are limited by position limits, leading to a finite number of unique strategies.
problem Limiting the number of long and short positions in trading strategies.
method Formulas and distributions derived for the number of unique trading strategies, transactions, and do-nothing actions.
result A discrete distribution of actions and their properties are presented.
I analyse the frequentist regret of the famous Gittins index strategy for multi-armed bandits with Gaussian noise and a finite horizon. Remarkably it turns out that this approach leads to finite-time regret guarantees comparable to those available for the popular UCB algorithm. Along the way I derive finite-time bounds…
The existence of optimal strategy in robust utility maximization is addressed when the utility function is finite on the entire real line. A delicate problem in this case is to find a "good definition" of admissible strategies, so that an optimizer is obtained. Under suitable assumptions, especially a time-consistency …
The paper examines how trading strategies lose value due to stock turnover.
problem Leakage of rank-dependent trading strategies due to stock turnover.
method Theoretical analysis and empirical estimation of leakage in discrete time.
result A new method to estimate leakage in trading strategies is introduced.
Solves expert prediction problem for 4 experts in finite time horizon.
problem Expert prediction problem in finite horizon with 4 experts.
method Solves nonlinear PDE, shows C2 solution, proves Nash equilibrium and regret conjectures. result Proves Finite vs Geometric regret conjecture for N=4 and shows comb strategies are optimal. We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. Th…
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas…
ES and FD gradients converge as optimization dimension grows.
problem Understanding the relationship between Evolution Strategies and Finite Differences gradients.
method Analyzing the convergence of gradients as the optimization dimension increases.
result ES and FD gradients converge as the dimension of the vector under optimization increases.
Optimal reinsurance strategies for multi-line insurance companies.
problem Choosing the best dynamic reinsurance policies for multi-line insurance companies.
method Characterized the optimal survival function as the unique nondecreasing viscosity solution of the HJB equation, solved numerically using the finite difference method.
result Provided proof of convergence of numerical solution to the survival probability function.
Optimal strategy found for constrained multi-armed bandit problems.
problem Constrained multi-armed bandit problems.
method Extended ε_t-greedy strategy with asymptotic optimality.
result Asymptotic optimality achieved with a simple strategy.
Paper optimizes aquaculture feeding and harvesting strategies for profit maximization.
problem Maximizing farm profit through optimal feeding and harvesting decisions under stochastic price dynamics.
method Developed a simplified aquaculture model and two numerical solution approaches: finite difference scheme and PINN-based method combined with DeepOS algorithm.
result PINN-based method achieves comparable accuracy to finite differences but is more scalable.
In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve according to quite general semimartingales. We show that the ruin problem corresponds to…
Study optimal consumption and investment strategies with constraints in a market with random coefficients.
problem Optimal consumption and investment strategies with constraints in a regime switching market with random coefficients.
method Explicit optimal strategies provided via solutions to new BSDE systems.
result Solving new BSDEs to find optimal values and strategies.
The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this question has been a focus of considerable attention over the last twenty years. We…
A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems that are expressed in terms of: the consumption plans' optimization problem in pure…
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.
Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.
problem Learning dynamics in zero-sum polymatrix games under different information settings.
method Two-timescale learning dynamics combining smoothed best-response updates and TD-learning for estimating local payoff functions.
result Polynomial-time finite-sample guarantees for convergence to an ε-Nash equilibrium in the minimal information case.
Optimizes dividend and reinsurance strategies for correlated insurance lines.
problem Stochastic control of optimal reinsurance and dividend policies for multiple insurance lines.
method Maximizes cumulative discounted dividends using a Hamilton-Jacobi-Bellman equation and finite difference method.
result Provides optimal strategies for transferring risk among reinsurers.
Study optimal strategies under uncertain market parameters and borrowing costs.
problem Optimal portfolio-consumption strategies in uncertain markets.
method Robust utility maximization framework with explicit solutions.
result Impacts of uncertain parameters, constraints, and borrowing costs quantified.
New discrete-time model shows insider trading dynamics.
problem Modeling insider trading with discrete time and noise traders.
method Formulated as a game with three types of traders, including an insider, noise traders, and a market maker. Proved existence of sequential Kyle equilibrium for various distributions and information flows.
result Equilibria exist in mixed strategies but not in pure strategies, unlike in Kyle's original model.
Optimal trade execution strategies show adaptive methods reduce costs.
problem Optimal trade execution with short-term price predictive signals.
method Comparison of static and adaptive strategies with transient and instantaneous market impacts.
result Adaptive strategies significantly reduce transaction costs compared to static strategies.
We give a method of constructing maps between tubular groups inductively according to a set of strategies. This map will be a quasi-isometry exactly when the set of strategies is consistent. Conversely, if there exists a quasi-isometry between tubular groups, then there is a consistent set of strategies for them. There…
Study stability of trading strategy under market perturbations.
problem Dynamic stability of trading strategy under market changes.
method Established reverse conjugacy characterizations, proved continuity and convergence of indirect utility process.
result Continuity and first-order convergence of indirect utility process under market perturbations.
New method detects heuristics in complex game strategies.
problem Understanding decision-making in games with infinite strategy spaces.
method Introducing decoupled strategies to detect convergence towards Nash equilibria.
result Predictive measure ΔD reveals participants' actions with high success rate.
Study on optimal strategies for minimizing shortfall risk in game options.
problem Existence of optimal hedging strategies for shortfall risk in game options.
method Continuous time Black--Scholes model, finite and infinite exercise times.
result Optimal strategies exist for finite exercise times but not for all time intervals.
Optimal dividend payout strategy found for Brownian risk model with ratcheting constraint.
problem Optimal dividend payout from a surplus process governed by Brownian motion with drift under ratcheting constraint.
method Solved a two-dimensional optimal control problem using viscosity solutions of Hamilton-Jacobi-Bellman equations.
result Threshold and curve strategies identified as optimal for different dividend rate sets.
The paper explores trading strategies using functional portfolio generation and arbitrage conditions.
problem Investigating arbitrage conditions for functional portfolio generation.
method Formulating conditions on trading strategies using Karatzas and Ruf's framework and applying a mollification argument.
result A general class of potential arbitrage strategies is identified.
This paper analyzes hedge errors in Black-Scholes models using finite difference techniques.
problem Accurate hedging strategies in dynamic market environments.
method Asymptotic approach and finite difference techniques.
result Reduction of hedge errors and enhancement of option pricing model robustness.
We present a new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring. In particular, the new algorithm achieves the minimax regret, within logarithmic factors, for both "easy" and "hard" problems. For easy problems, it additionally achieves logarithmic individual…
This work introduces COLA, a strategy to aggregate conformal prediction sets efficiently.
problem Efficiently combining multiple conformity scores to reduce prediction set size.
method Introduces COnfidence-Level Allocation (COLA) to optimally allocate confidence levels across sets.
result COLA achieves smaller prediction sets than state-of-the-art methods while maintaining valid coverage.
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid p…
AI optimizing for risk-adjusted return may choose unethical strategies.
problem AI optimization for risk-adjusted return may lead to unethical outcomes.
method Defined Unethical Odds Ratio (Υ) to calculate probability of unethical strategies, derived formula for limit as strategy space grows, provided algorithm for estimation.
result Probability of picking an unethical strategy can become high even with small proportion of unethical strategies.
A pairs trading model with time-varying volatility using stochastic control.
problem Optimizing pairs trading strategies with fluctuating asset volatilities.
method Stochastic control techniques, Finite Difference method, Generalized Method of Moments.
result Optimal trading strategies maximizing expected power utility from terminal wealth.
New strategies avoid forced exploration for unimodal bandits.
problem Optimal exploration of unimodal bandit problems.
method Adapting IMED strategy to unimodal structure without forced exploration.
result Proven optimal strategies for unimodal bandits.
Study long-term asset liquidation behavior with external flows.
problem Investigate optimal liquidation in presence of external flows.
method Convergence analysis of BSDEs for value function and strategy.
result Long-term liquidation may not occur due to external flows.
Finite quotients of fibered hyperbolic 3-manifold groups detect taut polynomials.
problem Detecting taut polynomials of fibered faces of Thurston norm balls
method Developing a framework for profinite invariance of twisted multivariable Alexander polynomials
result Proving finite quotients detect taut polynomials
SMG combines shuffling and momentum for non-convex optimization.
problem Non-convex finite-sum optimization problems.
method Shuffling Gradient-based method with momentum.
result Established state-of-the-art convergence rates for SMG.
We describe a natural strategy to enumerate compact hyperbolic 3-manifolds with geodesic boundary in increasing order of complexity. We show that the same strategy can be employed to analyze simultaneously compact manifolds and finite-volume manifolds having toric cusps. In opposition to this we show that, if one allow…
Geometric Mean Market Makers super-hedge impermanent loss without models.
problem Super-hedging impermanent loss in Geometric Mean Market Makers.
method Model-free rebalancing strategy.
result Loss-versus-rebalancing vanishes due to finite variation exchange rate.
Algorithm finds optimal investment strategies for non-differentiable preferences.
problem Optimal investment strategies under non-differentiable preferences.
method Reduces problem to a discrete grid, uses efficient method to find strategies.
result Optimal strategies lie on a discrete grid, allowing efficient computation.
Study excludes smooth actions on low-dimensional spheres for certain finite Oliver groups.
problem Excluding smooth effective one fixed point actions of finite Oliver groups on low-dimensional spheres.
method Strategy based on Oliver groups and Laitinen-Morimoto-Pawałowski results.
result Nonexistence of smooth effective one fixed point actions for specified finite Oliver groups.
Paper proves CMC hypersurfaces in R6 are minimal if they have finite index.
problem Proving complete noncompact CMC hypersurfaces in R6 are minimal.
method Proof strategy applicable to R4 and R5, providing alternative proofs.
result Proves complete noncompact CMC hypersurfaces in R6 with finite index are minimal.
Algorithm solves American options with regime-switching using multigrid and compact finite difference.
problem Pricing American put options with regime-switching.
method Multigrid iterative algorithm based on compact finite difference schemes and Hermite interpolation.
result The algorithm provides a fast and efficient tool for pricing American put options with regime-switching.
Study uses reinforcement learning to optimize trading strategies.
problem Developing an optimal execution strategy for traders.
method Reinforcement learning model using ABIDES simulator.
result Reinforcement learning model outperforms standard strategies.
Study explores strategies for randomized allocation in delayed rewards bandits.
problem Understanding the exploration-exploitation tradeoff in randomized strategies with delayed rewards.
method Examines two strategies: updating exploration sequence at every time point vs. updating only when a new reward is observed.
result The strategy updating only when a new reward is observed leads to strong consistency in allocation for a wider scope of situations.
Investigates optimal strategies for behavioral control problems with finite variation controls.
problem Behavioral singular stochastic control problems with finite variation controls.
method Abstract framework, applied to storage management and portfolio investment problems, using CPT preferences and Skorokhod representation theorem.
result Existence of optimal strategies for various goal functionals, including CPT preferences.
Study optimal liquidation strategies with infinite horizon and regime switching.
problem Optimal liquidation with semimartingale strategies in a stochastic environment.
method Characterization of value function and optimal strategy via BSDEs with infinite horizon.
result Existence and uniqueness of optimal control problem solutions.
Optimal dividend strategy in insurance with limited rate decrease.
problem Maximizing expected discounted dividends up to ruin in a risk model.
method Two-dimensional optimal control problem solved using Hamilton-Jacobi-Bellman equation.
result Value function is unique viscosity solution and can be approximated by ratcheting strategies.