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.
Study solves HJB equations for time-inconsistent control problems.
We consider a semilinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity which is related to a stochastic control problem with fuel constraint. The fuel constraint translates into a singular initial condition for the HJB equation. We first propose a transformation based on a change of vari…
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is contin…
New method uses TT approximations to solve HJB equations for efficient sampling.
Paper explores solving HJB equations using neural networks.
Solves pair trading problem using consumption-investment theory.
Deep neural nets approximate high-dimensional HJB equations efficiently.
In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent…
Proposes a new uncertain volatility model with worst-case scenario analysis.
We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic progr…
We introduce a dynamic credit portfolio framework where optimal investment strategies are robust against misspecifications of the reference credit model. The risk-averse investor models his fear of credit risk misspecification by considering a set of plausible alternatives whose expected log likelihood ratios are penal…
This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in [6] does not work. We invoke the HJB equation of this problem and give an explicit viscosity solution of…
Paper solves a complex stopping problem using regularization and HJB equations.
Study uses FEM for HJB in option pricing with borrowing fees, improving accuracy and efficiency.
Paper tackles time inconsistency in portfolio management with stochastic volatility and power utility.
The paper solves a complex financial optimization problem using a novel mathematical technique.
Optimal contracts are found for agents with quadratic effort costs.
Study bond market making with hit-ratio target using optimal control and HJB equations.
Study optimal stopping in random exploration, deriving HJB and designing a reinforcement learning algorithm.
Deep learning for HJB PDEs using synthetic data and residual minimization.
Model stock price dynamics using semi-Markov processes.
A new method solves complex financial equations efficiently.
We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solut…
Unified framework for growth models with environmental risk and pollution-dependent disasters.
In this paper, we study the dividend strategies for a shareholder with non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to the Markov strategies. This is a time inconsistent control problem. The extended HJB equation is given an…
Deep learning method proves convergence for high-dimensional PDEs.
Paper uses second-order differential geometry to study stochastic mechanics.
This paper investigates sufficient conditions for a Feynman-Kac functional up to an exit time to be the generalized viscosity solution of a Dirichlet problem. The key ingredient is to find out the continuity of exit operator under Skorokhod topology, which reveals the intrinsic connection between overfitting Dirichlet …
Study portfolio selection with exogenous and endogenous transaction costs using deep learning.
In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem [SIAM J. Fin. Math. (2011) 22-54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the HJB equation is a partial integro-diffe…
In this paper, we consider the problem of optimal investment by an insurer. The insurer invests in a market consisting of a bank account and risky assets. The mean returns and volatilities of the risky assets depend nonlinearly on economic factors that are formulated as the solutions of general stochastic different…
This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an Itô-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching. Then, by using …
Optimal credit and consumption strategies in a switching market with default contagion.
Paper tackles DOCTR-L with SciPhy RL, solving neural PDEs from data.
Paper solves Bayesian bandit problem with continuous-time limit and approximate policy.
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows us to numerically solve stochastic control problems with controlled volatility,…
Study optimizes dividend payout strategies under fluctuating interest rates.
This work develops efficient methods for continuous-time distributional reinforcement learning.
Investor selects portfolios based on news attention in a hidden Markov model.
The paper studies scaling limits of hedging prices in financial models.
In this paper we investigate a dynamic stochastic portfolio optimization problem involving both the expected terminal utility and intertemporal utility maximization. We solve the problem by means of a solution to a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) equation. We propose the so-called Riccati met…
Deep-MacroFin uses neural networks to solve complex economic models efficiently.
We introduce Taylor expansions that do not require the differentiability. We also provide new solutions to partial differential equations. We apply our methods to finance.
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash equilibrium for a large, but finite, number of players. The method, also explained in…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the value function for general utility functions, we rely on the dynamic programming app…
Study optimal consumption and investment strategies with leverage constraints using Epstein-Zin utility.
Develops a new method for pricing GMWBs with jumps and stochastic interest rates.
We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky asset. Using stochastic control, we characterize the value function as the unique cla…