This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the per…
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48 results for “discrete strategies”
Study robust optimization for discrete strategies under uncertain conditions.
problem Optimizing decisions in uncertain environments with discrete strategies.
method Nonconcave robust optimization with discrete constraints.
result Existence of maximizers under specific conditions.
Proves existence of a strategy to minimize shortfall for game options.
problem Minimizing shortfall for game options in discrete time.
method Proves existence of a self-financing strategy.
result Existence of a self-financing strategy to minimize shortfall for game options in discrete time.
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…
Study of discrete-time mean-variance model using reinforcement learning.
problem Discrete-time model with more general return distribution assumptions.
method Entropy-based exploration cost, reinforcement learning algorithm design.
result Optimal investment strategy with Gaussian density function.
Study evaluates discretized arbitrage strategies in fractional financial markets.
problem Serial correlation in financial markets with fractional Brownian motion.
method Revisit and transfer Shiryaev and Salopek's strategies to a real-world setting, distretizing dynamics and introducing transaction costs.
result Both strategies are promising with respect to terminal portfolio values and loss probabilities.
Discrete time multi-period mean-variance model: Bellman type strategy and Empirical analysisq-fin.MF
Paper introduces dynamic strategies for multi-period investment models.
problem Optimizing investment strategies over multiple periods with risk and return considerations.
method Developed a Bellman principle for discrete time multi-period mean-variance models, leading to dynamic optimal strategies and efficient frontiers.
result Dynamic optimal strategies can achieve higher returns with lower risk compared to the 1/n strategy.
Optimal strategy for liquidating portfolios under discrete time intervals.
problem Optimizing liquidation of portfolios with discrete time constraints and impact effects.
method Modeling portfolio liquidation with N risky assets, using VaR for cost measurement, and deriving an optimal liquidation time.
result The optimal liquidation time is only influenced by temporary price impacts, not permanent ones.
NES optimizes discrete structured VAEs effectively without gradient propagation.
problem Learning high-dimensional discrete latent spaces in generative models.
method Natural Evolution Strategies (NES) for gradient-free optimization of discrete structures.
result NES effectively optimizes discrete structured VAEs, comparable to gradient-based methods.
Study optimal hedging for claims with random weights in discrete time.
problem Optimal hedging for claims with random weights in discrete time.
method Explicit recursive representation of optimal hedging strategy, without ND condition.
result Obtained explicit optimal hedging strategy in a recursive form.
Semistatic trading strategies can be taken to limits in discrete time.
problem Limits of semistatic trading strategies in discrete time.
method Analysis in full generality for a two-period model, and under a probabilistic condition for multi-period, multi-stock models.
result Pointwise limits of semistatic trading strategies are again semistatic strategies.
Study resolves time consistency in mean-standard deviation stopping problem for discrete time.
problem Time consistency in mean-standard deviation stopping problem for discrete time.
method Formulated as subgame perfect Nash equilibrium, considering liquidation strategies.
result Equilibrium liquidation strategy always exists, but optimal strategies may not.
In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…
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.
A game theory study on optimal hiding and searching strategies in discrete locations.
problem Optimal hiding and searching strategies in a two-person zero-sum game between a hider and a searcher.
method Proved the existence of optimal strategies, developed an algorithm to compute them, and compared with a simple strategy.
result Optimal hiding strategy involves hiding in each location with nonzero probability, and optimal searching strategy can be constructed with up to n simple sequences.
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.
Traders in a Strange Land: Agent-based discrete-event market simulation of the Figgie card gameq-fin.TR
Study Figgie card game strategies using agent-based simulation.
problem Analyze strategies for Figgie card game and market behavior.
method Develop agent-based discrete-event market simulation to test strategies.
result Fundamentalist strategy is profit-maximizing in all tested combinations.
This text explores strategies for learning discrete latent structures in neural networks.
problem Learning discrete latent structures in neural networks is challenging.
method Continuous relaxation, surrogate gradients, and probabilistic estimation.
result Many latent structure learning strategies use the same fundamental building blocks but apply them differently.
Optimizes portfolios with costs, showing existence of optimal strategies.
problem Risk-sensitive portfolio optimization with transaction costs.
method Log-return i.i.d. framework, Bellman equation analysis.
result Existence of optimal strategies for risk-averse and risk-seeking cases.
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile he…
We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition t…
We construct algorithms for computation of prices and superhedging strategies for game options in general discrete markets both from the seller and the buyer points of view.
Random Gaussian noise and pixel discretization improve image classifier robustness.
problem Whitebox adversarial attacks decrease classifier accuracy.
method Inject random Gaussian noise, discretize pixels, and use any classifier.
result Reduces KL divergence and lower bound on classifier accuracy.
Investment strategy optimization from discrete to continuous models.
problem Optimizing investment strategies and stopping times in both continuous and discrete settings.
method Characterized value functions via quadratic reflected BSDEs for continuous case, discretized BSDEs for discrete case, and derived uniform convergence rates.
result Uniform convergence and rate from discrete to continuous quadratic reflected BSDEs.
Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strate…
We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Levy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice …
Paper develops a continuous-time framework for financial markets without stochastic calculus.
problem Developing continuous-time financial models without stochastic calculus.
method A general framework using conditional topologies and pseudo-distance topologies.
result No-arbitrage conditions hold in continuous time if and only if they hold in discrete time.
We develop a polynomial method to optimize trading in markets with transaction costs.
problem Optimizing trading strategies in markets with proportional transaction costs.
method Polynomial approximation of the residual value function to determine optimal trading strategies.
result Identify the trade-off between trading frequency and trade sizes for satisfactory agreement with theoretically optimal strategies.
We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game wh…
New method reduces discrete flow transitions, improving perplexity estimation.
problem Stochasticity in discrete paths makes rectification strategies ineffective.
method Dynamic-optimal-transport-like minimization objective with minibatch strategies.
result 32 times reduction in transitions for same perplexity.
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …
Sharp bounds for high-probability estimation of discrete distributions.
problem Estimating discrete distributions with high probability under -divergence.
method Sharp upper and lower bounds for the classical Laplace estimator, and characterization of minimax high-probability risk for any estimator.
result Sharp bounds for high-probability estimation of discrete distributions can be achieved through a simple smoothing strategy.
Bayesian networks are convenient graphical expressions for high dimensional probability distributions representing complex relationships between a large number of random variables. They have been employed extensively in areas such as bioinformatics, artificial intelligence, diagnosis, and risk management. The recovery …
Study optimal investment strategies under model uncertainty in discrete markets.
problem Maximizing utility in markets with model uncertainty.
method Alternative framework for model uncertainty, using stochastic processes.
result Optimal investment strategies exist under certain conditions.
An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Banditscs.AI
Optimal regret achieved in stochastic, discrete multi-armed bandits using information-theoretic exploration.
problem Optimal exploration vs. exploitation in stochastic, discrete multi-armed bandits.
method Proposes an information-theoretic strategy based on the value of information criterion, using simulated-annealing-like updates of a parameter.
result Achieves logarithmic optimal regret with respect to the number of episodes.
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.
Study examines pricing strategies in competitive supply chains with discrete prices.
problem Inaccurate assumptions in traditional SC models for pricing decisions.
method Examines a SC model with one supplier and two manufacturers, considering customer demand segmentation and discrete price setting.
result Nash equilibria among manufacturers are not unique, and low denomination factors can lead to instability.
Paper proposes a new algorithm for efficient hyper-parameter optimization.
problem Efficient hyper-parameter tuning for machine learning models.
method Information geometric optimization with stochastic natural gradient for discrete search domains.
result The proposed algorithm achieves faster optimization than existing methods without manual tuning.
Study efficient rebalancing strategies for portfolio tracking error.
problem Optimizing portfolio rebalancing under high-frequency asset price models.
method Discrete-time rebalancing strategies derived from continuous model.
result Asymptotically efficient sequence of simple strategies.
We present extremal constructions connected with the property of simplicial collapsibility. (1) For each , there are collapsible (and shellable) simplicial -complexes with only one free face. Also, there are non-evasive -complexes with only two free faces. (Both results are optimal in all dimensions.) (2…
The paper proves convergence of discrete maps to Riemann mappings for polyhedral surfaces.
problem Discrete conformal geometry of polyhedral surfaces.
method Establishing rigidity for hexagonal triangulations and estimating quasiconformal constants.
result Discrete conformal maps converge to Riemann mappings for Jordan domains.
One-Dimensional Pricing of CPPIq-fin.PR
Constant Proportion Portfolio Insurance (CPPI) is an investment strategy designed to give participation in the performance of a risky asset while protecting the invested capital. This protection is however not perfect and the gap risk must be quantified. CPPI strategies are path-dependent and may have American exercise…
We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us to derive the no-regret properties of a large class of discrete-time algorithms i…
This work bounds the generalization error of private algorithms for discrete data.
problem Bounding the generalization error of private algorithms for discrete data.
method Information-theoretic approach using relative entropy and the method of types.
result Explicit upper bounds on the generalization error of stable private algorithms for discrete data.
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.
Constructive no-arbitrage criterion under transaction costs in the case of finite discrete timemath.PR
We obtain a constructive criterion for robust no-arbitrage in discrete-time market models with transaction costs. This criterion is expressed in terms of the supports of the regular conditional upper distributions of the solvency cones. We also consider the model with a bank account. A method for construction of arbitr…
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the expected shortfall under a cost constraint and show that these problems can be trea…
Study optimal liquidation strategies on Uniswap v2/v3 considering price impact.
problem Optimal liquidation of large positions on Uniswap v2/v3 under transient price impact.
method Dynamic programming and numerical approximation for Uniswap v3, closed-form solutions for v2.
result Obtained optimal strategies for both Uniswap v2 and v3, showing how liquidity profile influences them.