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.
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do…
In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward …
The paper optimizes portfolios in a financial market with correlated assets using a stochastic volatility model.
problem Optimizing portfolios in a financial market with correlated assets and stochastic volatility.
method Derive a Hamilton-Jacobi-Bellman equation, use approximation methods, analyze value function using expansion of utility function, control error with second-order terms, generate close-to-optimal portfolio.
result Close-to-optimal portfolio generated using first-order approximation of utility function with controlled error.
This paper is devoted to obtaining a wellposedness result for multidimensional BSDEs with possibly unbounded random time horizon and driven by a general martingale in a filtration only assumed to satisfy the usual hypotheses, i.e. the filtration may be stochastically discontinuous. We show that for stochastic Lipschitz…
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…
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 …
Study optimal portfolio management with periodic evaluations in stochastic models, considering convex constraints.
problem Optimal portfolio management under ratio-type periodic evaluations in stochastic factor models with convex trading constraints.
method Transformed infinite horizon optimal control problem into an auxiliary terminal wealth optimization problem. Introduced an auxiliary unconstrained optimization problem in a modified market model. Used martingale duality approach to establish dual minimizer and optimal unconstrained wealth process.
result Derived and verified the optimal constrained portfolio process for the original problem over an infinite horizon.
This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using tools from stochastic control, and how to rigorously verify their optimality by mea…
In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span Δt, say one week or one year. This measures how well (or how bad) the asset performs over that given period of time. It has been established tha…
In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional RBSDEs) and show that a value function of the optimal switching under ambiguity …
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…
The study introduces anytime learning schedules for large language models without fixed horizons.
problem Training large language models without knowing the total training horizon.
method Theoretical analysis and weight averaging to create anytime learning schedules.
result Theoretical and empirical evidence shows that weight averaging with simple step sizes can achieve comparable final loss to well-tuned cosine schedules.
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 optimal portfolios in a non-Markovian regime-switching model with random time horizon.
problem Optimal portfolio selection in a market with non-Markovian regime-switching and random time horizon.
method Formulated as a constrained stochastic linear-quadratic optimal control problem, derived closed-form expressions for optimal portfolios and efficient frontier.
result Closed-form expressions for optimal portfolios and efficient frontier derived under non-Markovian regime-switching and random time horizon.
Careful tuning of the learning rate, or even schedules thereof, can be crucial to effective neural net training. There has been much recent interest in gradient-based meta-optimization, where one tunes hyperparameters, or even learns an optimizer, in order to minimize the expected loss when the training procedure is un…
We extend the model of stochastic bandits with adversarial corruption (Lykouriset al., 2018) to the stochastic linear optimization problem (Dani et al., 2008). Our algorithm is agnostic to the amount of corruption chosen by the adaptive adversary. The regret of the algorithm only increases linearly in the amount of cor…
We study the online estimation of the optimal policy of a Markov decision process (MDP). We propose a class of Stochastic Primal-Dual (SPD) methods which exploit the inherent minimax duality of Bellman equations. The SPD methods update a few coordinates of the value and policy estimates as a new state transition is obs…
Proposes a model for multi-horizon probabilistic forecasting of time series influenced by asynchronous events.
problem Forecasting time series influenced by asynchronous events is challenging.
method Introduces Variational Synergetic Multi-Horizon Network (VSMHN), a deep conditional generative model combining deep point processes and variational recurrent neural networks.
result Produces accurate, sharp, and realistic probabilistic forecasts.
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…