A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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…
Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under th…
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent …
A new ML algorithm solves complex economic control problems.
New RL method learns K-step lookahead Q-functions for fixed-horizon MDPs.
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…
Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.
Study long-term asset liquidation behavior with external flows.
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, to stu…
Study on BSDEs with random time horizon, focusing on existence and properties.
We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obt…
Optimal reinsurance and dividend strategy for insurance companies in a finite time.
Study optimal consumption with drawdown limits over a fixed time frame.
Developed LQ MFG theory with common noise, proving existence and uniqueness.
Paper analyzes convergence of dynamic policy gradient for MDPs, improving performance in finite-time problems.
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…
We aim to generalize the results of Cai and Nitta (2007) by allowing both the utility and production function to depend on time. We also consider an additional intertemporal optimality criterion. We clarify the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attain…
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form formula for a trading strategy which approximates the optimal trading strategy whe…
Develops a regression approach for solving MDPs with general state and action spaces.
Extends RL to random stopping times, improving optimization.
Derives time-averaged active inference from control principles.
A new Bayesian method optimizes time-dependent expensive functions with lookahead.
Deep neural nets approximate random dynamical system trajectories uniformly in time.
In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options…
I introduce and analyse an anytime version of the Optimally Confident UCB (OCUCB) algorithm designed for minimising the cumulative regret in finite-armed stochastic bandits with subgaussian noise. The new algorithm is simple, intuitive (in hindsight) and comes with the strongest finite-time regret guarantees for a hori…
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.
We consider a finite-horizon multi-armed bandit (MAB) problem in a Bayesian setting, for which we propose an information relaxation sampling framework. With this framework, we define an intuitive family of control policies that include Thompson sampling (TS) and the Bayesian optimal policy as endpoints. Analogous to TS…
The paper clarifies long-horizon investment and DCA, showing no risk reduction but different exposure profiles.
Kernel-UCBVI algorithm balances exploration and exploitation in metric state-action spaces.
Optimizes portfolio in volatile markets with jumps, providing accurate formulas.
Solves optimal stopping for Gauss-Markov bridges using time-space transformation.
Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.
New algorithms learn MDPs with better regret bounds using generative sampling.
Logarithmic regret for continuous-time reinforcement learning.
Paper identifies reductive MDPs, solving them in polynomial time.
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level ) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only…
Firms miscount their customers who stop buying without saying goodbye.
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…
In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volu…
This paper improves Thompson Sampling for complex decision-making problems.
New algorithm achieves asymptotically optimal regret without horizon dependence.
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential equations into the theoretical framework of diffusion approximation, extending the …
Study examines Wang-Yau quasi-local energy in strong fields near apparent horizons.
We study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The firm aims to maximize its expected total net profit by choosing the optimal inve…
The paper optimizes portfolios in a financial market with correlated assets using a stochastic volatility model.
In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The mode…
This paper examines the value of a cancellable European option in a finite time horizon setting. The specifications of this generalized European option allow the seller to cancel the option at any point in time for a fixed penalty paid directly to the holder. Here, we provide an explicit valuation formula for the Europ…