Results 111 to 120 of about 87,102,086 (248)

Reinforcement Learning for Jump‐Diffusions, With Financial Applications

Mathematical Finance, EarlyView.
ABSTRACT We study continuous‐time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump‐diffusion processes. We formulate an entropy‐regularized exploratory control problem with stochastic policies to capture the exploration–exploitation balance essential for RL.
Xuefeng Gao, Lingfei Li, Xun Yu Zhou
wiley   +1 more source

Equilibrium Reward for Liquidity Providers in Automated Market Makers

Mathematical Finance, EarlyView.
ABSTRACT We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader–follower stochastic game, where the venue is the leader and a representative LP is the follower.
Alif Aqsha, Philippe Bergault, Leandro Sánchez‐Betancourt   +2 more
wiley   +1 more source

A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE

Stochastic Processes and their Applications, 2004
The first part of the paper deals with Markov processes generated by time-inhomogeneous uniformly elliptic differential operators on \(\mathbb R^N\) in a divergence form, i.e.\ \(L=\partial _i(a_{ij}(t,x)\partial _j)+b_i(t,x)\partial _i\) where the coefficients \(a\) and \(b\) are measurable and uniformly bounded. It is shown that, indeed, there exists
openaire   +1 more source

Relative Arbitrage Opportunities With Interactions Among N Investors

Mathematical Finance, EarlyView.
ABSTRACT The relative arbitrage portfolio outperforms a benchmark portfolio over a given time‐horizon with probability one. With market price of risk processes depending on the market portfolio and investors, this paper analyzes the multi‐agent optimization of relative arbitrage opportunities in the coupled system of market and wealth dynamics.
Tomoyuki Ichiba, Nicole Tianjiao Yang
wiley   +1 more source

Optimal energy growth lower bounds for a class of solutions to the vectorial Allen-Cahn equation [PDF]

, 2014
We prove optimal lower bounds for the growth of the energy over balls of minimizers to the vectorial Allen-Cahn energy in two spatial dimensions, as the radius tends to infinity. In the case of radially symmetric solutions, we can prove a stronger result
Sourdis, Christos
core  

Market Making With Fads, Informed, and Uninformed Traders

Mathematical Finance, EarlyView.
ABSTRACT We characterize the solution to a continuous‐time optimal liquidity provision problem in a market populated by informed and uninformed traders. In our model, the asset price exhibits fads —these are short‐term deviations from the fundamental value of the asset.
Emilio Barucci, Adrien Mathieu, Leandro Sánchez‐Betancourt   +2 more
wiley   +1 more source

Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces

Journal of Differential Equations
We prove global Hölder regularity result for weak solutions $u\in N^{1,p}(Ω, μ)$ to a PDE of $p$-Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nabla u|^{p-2}\nabla u \right)=\overlineν, \] where ...
Luca Capogna, Ryan Gibara, Riikka Korte, Nageswari Shanmugalingam   +3 more
openaire   +3 more sources

Existence of weak solutions to an anisotropic electrokinetic flow model [PDF]

In this article we present a system of coupled non-linear PDEs modelling an anisotropic electrokinetic flow. We show the existence of suitable weak solutions in three spatial dimensions, that is weak solutions which fulfill an energy inequality, via a ...
Plato, Luisa, Hömberg, Dietmar, Lasarzik, Robert   +2 more
core   +1 more source

Information‐Theoretic Approach to Financial Market Modeling

Mathematical Finance, EarlyView.
ABSTRACT The paper treats the financial market as a communication system, using four information‐theoretic assumptions to derive an idealized model with only one parameter. State variables are scalar stationary diffusions. The model maximizes the surprisal of the market and minimizes the Kullback–Leibler divergence between the benchmark‐neutral pricing
Eckhard Platen
wiley   +1 more source

Representation of Forward Performance Criteria with Random Endowment via FBSDE and Its Application to Forward Optimized Certainty Equivalent

Mathematical Finance, EarlyView.
ABSTRACT We extend the notion of forward performance criteria to settings with random endowment in incomplete markets. Building on these results, we introduce and develop the novel concept of forward optimized certainty equivalent (forward OCE), which offers a genuinely dynamic valuation mechanism that accommodates progressively adaptive market model ...
Gechun Liang, Yifan Sun, Thaleia Zariphopoulou   +2 more
wiley   +1 more source