Study state-dependent Hawkes processes for limit order book modeling.
problem Modeling feedback loop between order flow and limit order book shape.
method Existence and uniqueness of state-dependent Hawkes processes, simulation, maximum likelihood estimation.
result Excitation effects in order flow are strongly state-dependent.
A Hawkes process with state-dependent factor models order flows in limit order books.
problem Modeling order flows in limit order books for better market prediction.
method A Hawkes process with a state-dependent factor for conditional intensity estimation.
result State-dependent formulations improve the fit of LOB models to financial data.
The paper extends intensity models for limit order books using marked point processes.
problem Modeling intensity ratios in limit order books with state dependency and clustering.
method Developed a new model combining three multiplicative components for marked point processes.
result The new model outperforms other intensity-based methods in predicting market order signs and aggressiveness.
Proposes a model for simulating limit order books with state-dependent intensities.
problem Simulating the dynamics of limit order books with varying intensities of order submission.
method Developed a parametric model with state-dependent intensities for limit orders, market orders, and cancellations. Introduced new models for order placement and cancellation selection.
result The proposed model accurately simulates the dynamics of limit order books and outperforms standard Poisson models.
New algorithm speeds up MCMC for complex distributions.
problem Efficient sampling from complex, high-dimensional distributions.
method Numerical Generalized Randomized Hamiltonian Monte Carlo with state-dependent event rates.
result Approximates Hamiltonian trajectories for robust sampling.
Measures price impact in order-driven markets without relying on averages.
problem Measuring price impact in order-driven markets without relying on averages.
method Modeling the limit order book using state-dependent Hawkes processes and defining price impact profile as a function of the compensator of a stochastic process.
result The clustering of sell child orders has a bigger impact on price than their sizes.
In this paper, we consider the asset-liability management under the mean-variance criterion. The financial market consists of a risk-free bond and a stock whose price process is modeled by a geometric Brownian motion. The liability of the investor is uncontrollable and is modeled by another geometric Brownian motion. W…
In this article, we consider a Markov process X, starting from x and solving a stochastic differential equation, which is driven by a Brownian motion and an independent pure jump component exhibiting state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability …
In a dual risk model, the premiums are considered as the costs and the claims are regarded as the profits. The surplus can be interpreted as the wealth of a venture capital, whose profits depend on research and development. In most of the existing literature of dual risk models, the profits follow the compound Poisson …
We reduce variance in RL with input-dependent baselines.
problem High variance in RL with standard baselines in input-driven environments.
method Derive and use a bias-free, input-dependent baseline; propose a meta-learning approach.
result Input-dependent baselines improve training stability and policy quality.
Proposes a new framework for optimizing utility with state-dependent benchmarks.
problem Various interpretations of benchmarks in utility functions.
method General framework of state-dependent utility optimization with stochastic benchmarks.
result Provides optimal solutions and addresses issues of well-definedness and feasibility.
Unique optimal strategy identified for state-dependent risk aversion.
problem Consistency of optimal portfolio choice for varying risk aversion.
method Analysis of state-dependent exponential utilities in arbitrage-free markets.
result Uniqueness of optimal strategy across any time horizon.
Study of SGD with state-dependent noise, improving escape from local minima.
problem Understanding and improving the dynamics of SGD in non-convex optimization.
method Formal study on SGD with state-dependent noise, proposing power-law dynamic with state-dependent diffusion.
result Power-law dynamic can escape from sharp minima exponentially faster than flat minima.
A framework combining HSMM and survival analysis for lifecycle-oriented mobility analysis.
problem Understanding individual metro usage dynamics over multi-year horizons.
method A state-based lifecycle modeling framework integrating HSMM and discrete-time survival analysis.
result Identification of interpretable mobility states, transition dynamics, and state-dependent exit and re-entry processes.
Study controlled contagion with state-dependent killing, proving a comparison principle.
problem Analyzing controlled McKean--Vlasov contagion with state-dependent killing.
method Proof of a comparison principle using Wasserstein smooth-gauge comparison and killing-jump absorption estimates.
result Established a comparison principle for the two-population killed-particle HJB.
Neural Lévy model improves risk and density forecasting for financial returns.
problem Financial returns exhibit heavy tails, volatility clustering, and jumps.
method Proposes a neural Lévy jump-diffusion framework that learns conditional drift, diffusion, jump intensity, and size distribution.
result Demonstrates improved calibration, sharper tail control, and risk reduction.
A new model predicts bid-ask spread dynamics in financial markets.
problem Capturing the self-exciting nature of bid-ask spread changes.
method State-dependent Spread Hawkes model (SDSH) incorporating various spread jump sizes and current state impact.
result The SDSH model accurately forecasts spread values at short-term horizons.
Theory integrates loss aversion into expected utility for monetary returns.
problem Modeling loss aversion in expected utility theory.
method Develops state-dependent linear utility functions incorporating loss aversion.
result Contracts from monopolists in insurance markets.
We revisit Merton's portfolio optimization problem under boun-ded state-dependent utility functions, in a market driven by a Lévy process Z extending results by Karatzas et. al. (1991) and Kunita (2003). The problem is solved using a dual variational problem as it is customarily done for non-Markovian models. One of …
This paper improves credit risk analysis by incorporating state-dependent recovery rates into a factor model.
problem Accurate default forecasting in credit risk analysis.
method Extends a one-factor Gaussian copula model to include state-dependent recovery rates and a common factor.
result The proposed model outperforms other models in default prediction, especially during hectic periods.
Introduces a new class of hybrid processes combining Markov chains and Hawkes processes.
problem Characterize and ensure existence and uniqueness of complex hybrid marked point processes.
method Defines hybrid marked point processes implicitly via intensity and state process interactions, proving existence and uniqueness under general assumptions.
result Proves existence and uniqueness of hybrid marked point processes, extending existing results.
Study efficient algorithms for nonconvex optimization with state-dependent Markov data.
problem Stochastic optimization with Markovian data and state-dependent transition kernels.
method Projection-based and projection-free algorithms for constrained nonconvex problems.
result The number of oracle calls to achieve an ε-stationary point is O(1/ε2.5). Bayesian method calibrates local volatility with Gaussian processes.
problem Calibrating local volatility models is challenging.
method Bayesian inference with Gaussian process priors.
result Rich probabilistic model of local volatility with uncertainty.
The paper defines and characterizes conditional nonlinear expectations.
problem Defining and characterizing conditional nonlinear expectations.
method Embedding in decision theory, using state-dependent preferences, and continuous utility representation.
result Consistent backward conditional projections are characterized by the Sure-Thing Principle.
The paper tackles model-based RL's inaccuracy issue by dynamically adjusting planning horizons.
problem Model-based RL's failure due to model inaccuracy over long planning horizons.
method State-dependent planning horizon, learning cumulative model errors with Temporal Difference methods.
result The proposed method successfully adapts planning horizons to state-dependent model accuracy, improving policy learning efficiency.
Study of Langevin processes and their convergence rates for non-convex problems.
problem Convergence of Langevin processes and SGD for non-convex optimization problems.
method Quantitative analysis of convergence rates for discrete Langevin-like processes.
result The convergence of SGD for non-convex problems depends on the potential function and additive noise.
Paper proposes ExsdHawkes to model LOBs, capturing volatility dynamics.
problem Modeling volatility signature plots in LOBs with high-frequency trading dynamics.
method Extended State-Dependent Hawkes Process (ExsdHawkes) with relaxed constraints.
result ExsdHawkes uniquely reproduces volatility signature plots, identifying MLOs as catalysts.
New method approximates diffusion process posteriors using moment functions.
problem Approximating posteriors of stochastic differential equations.
method Constructs variational process as controlled prior, approximates posterior with moment functions, uses natural gradient descent.
result Richer variational approximations for state-dependent diffusion terms.
We propose a new approach to utilities that is consistent with state-dependent utilities. In our model utilities reflect the level of consumption satisfaction of flows of cash in future times as they are valued when the economic agents are making their consumption and investment decisions. The theoretical framework use…
Distributed strategic learning has been getting attention in recent years. As systems become distributed finding Nash equilibria in a distributed fashion is becoming more important for various applications. In this paper, we develop a distributed strategic learning framework for seeking Nash equilibria under stochastic…
Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy …
The paper analyzes fill probabilities in limit order books with varying price levels.
problem Determining the likelihood of limit orders being executed in a limit order book.
method Developed a state-dependent stochastic framework to model limit order book dynamics.
result Derived semi-analytical expressions for fill probabilities and mid-price changes.
In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching Lévy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit expression for the value function. The solution of the corresponding first passage problem…
We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or sup…
Self-regulating annealing improves sampling from heavy-tailed datasets.
problem Sampling from heavy-tailed distributions using diffusion models.
method Proposed an SDE-based sampler with a state-dependent diffusion coefficient.
result State dependence induces a self-regulating annealing mechanism.
A new model for forward curves captures behavior through a single equation.
problem Modeling forward curves in a complex function space.
method Developed a stochastic partial differential equation with locally state-dependent coefficients.
result The model retains simplicity while capturing entire forward curve behavior.
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
New model considers wealth and time affecting risk aversion in portfolio selection.
problem Optimal investment strategy and consumption process depend on wealth and future income balance.
method Proposed a new mean-variance-utility framework with time and state-dependent risk aversion, solved using game theory.
result Equilibrium investment and consumption policies derived, aligning with investor behavior.
We develop a new method to estimate failure probabilities in complex systems.
problem Estimating failure probabilities in safety-critical autonomous systems is challenging due to the rarity of failures and large state spaces.
method We propose an adaptive importance sampling algorithm that minimizes forward Kullback-Leibler divergence and uses Markov score ascent methods.
result Our method provides more accurate failure probability estimates than existing techniques.
This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete. the prices of financial assets are modeled by Itô processes. The dynamic risk constr…
New method handles complex systems with discontinuous, heavy-tailed noise.
problem Handling discontinuous, heavy-tailed Lévy noise in stochastic systems.
method Developed nonlocal Kramers-Moyal formulas for SDEs with multiplicative Lévy noise.
result Validated framework for discovering interpretable SDE models from data.
Paper solves time-inconsistent control problems with BSDEs.
problem Time-inconsistent stochastic control in continuous time.
method Probabilistic representation via BSDEs.
result Equilibrium value function resolved for inconsistent cases.
Investor optimizes portfolio under dynamic risk preferences.
problem Optimizing investment under uncertain future risk attitudes.
method Developed a general equilibrium framework and solved for subgame-perfect equilibrium policies.
result Equilibrium policies include a novel hedging component to counteract anticipated risk aversion changes.
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
problem Capturing empirical phenomena like return skewness, heavy tails, and volatility asymmetry in option pricing models.
method Developing the Geometric Asymmetric Brownian Motion (GABM) within the Bachelier--Black--Scholes--Merton framework.
result Deriving closed-form option pricing formulas and a discrete-time binomial tree algorithm that converges to the GABM limit.
Study optimal control of diffusion processes with infimum or supremum costs.
problem Optimizing control of a diffusion process with costs dependent on its infimum or supremum.
method Introduced novel integral operators to solve two-dimensional singular control problems.
result Explicit solutions for optimal dividend problem with time-dependent preferences.
The paper solves a consumption-investment problem with state-dependent lower bounds.
problem A life-time consumption-investment problem with a state-dependent lower bound on consumption.
method Transformed the problem into a state-independent control problem to apply standard theory.
result Explicit optimal strategies provided for both homogeneous and non-homogeneous constraints.
New volatility model for option pricing with time-varying risk premium.
problem Volatility risk premium is time-varying and not well captured by existing models.
method Combines Markov switching with Realized GARCH framework to derive a state-dependent pricing kernel.
result The model reduces option pricing errors by 15% or more compared to competing models.
The paper proposes a machine learning approach for state-dependent asset allocation.
problem Market conditions cause performance deviations from long-term averages.
method Analyzes historical market states and asset returns to directly relate state variables to portfolio weights.
result The proposed approach generates a more efficient portfolio compared to traditional methods.