We consider the problem of numerical approximation for forward-backward stochastic differential equations with drivers of quadratic growth (qgFBSDE). To illustrate the significance of qgFBSDE, we discuss a problem of cross hedging of an insurance related financial derivative using correlated assets. For the convergence…
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48 results for “Quadratic Drivers”
In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple where is a semimartingale, and are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of …
We investigate a class of quadratic-exponential growth BSDEs with jumps. The quadratic structure introduced by Barrieu & El Karoui (2013) yields the universal bounds on the possible solutions. With local Lipschitz continuity and the so-called A_gamma-condition for the comparison principle to hold, we prove the existenc…
This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo…
We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility. Our approach is based on martingale methods which rely on recent results on the e…
Investor optimizes utility in a market with endogenous pricing.
problem Maximizing utility in an incomplete market with endogenous pricing.
method Characterized optimality via FBSDEs and BSPDEs using generalized subgradients.
result Existence and smoothness of solutions for optimal investment and FBSDEs.
Advanced driver assistance systems (ADAS) can be significantly improved with effective driver action prediction (DAP). Predicting driver actions early and accurately can help mitigate the effects of potentially unsafe driving behaviors and avoid possible accidents. In this paper, we formulate driver action prediction a…
Reflected backward stochastic differential equations and a class of non linear dynamic pricing ruleq-fin.PR
In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of -Snell enveloppe. Then, in a second step, we re…
We demonstrate that the use of asymptotic expansion as prior knowledge in the "deep BSDE solver", which is a deep learning method for high dimensional BSDEs proposed by Weinan E, Han & Jentzen (2017), drastically reduces the loss function and accelerates the speed of convergence. We illustrate the technique and its imp…
Financial Resilience Evaluation: From Conditional Expectations to Dynamic Convex Risk Measuresq-fin.MF
Enhances resilience evaluation by using dynamic convex risk measures.
problem Capturing the full risk profile of financial positions under adverse conditions.
method Introduces a new resilience evaluation method using dynamic convex risk measures.
result Shows that the resilience evaluation can distinguish between positions with the same expected recovery but different conditional risk profiles.
Neural Brownian Motionmath.PR
Introduces Neural-Brownian Motion for modeling dynamics under learned uncertainty.
problem Modeling dynamics under uncertainty with learned parameters.
method Defines NBM using a neural network to replace classical martingale property with a non-linear expectation operator.
result Proves existence and uniqueness of canonical NBM as a continuous -martingale.
Vacant taxi drivers' passenger seeking process in a road network generates additional vehicle miles traveled, adding congestion and pollution into the road network and the environment. This paper aims to employ a Markov Decision Process (MDP) to model idle e-hailing drivers' optimal sequential decisions in passenger-se…
In this paper we consider a class of BSDEs with drivers of quadratic growth, on a stochastic basis generated by continuous local martingales. We first derive the Markov property of a forward--backward system (FBSDE) if the generating martingale is a strong Markov process. Then we establish the differentiability of a FB…
The potential positive impact of autonomous driving and driver assistance technolo- gies have been a major impetus over the last decade. On the flip side, it has been a challenging problem to analyze the performance of human drivers or autonomous driving agents quantitatively. In this work, we propose a generic method …
Data generated by cars is growing at an unprecedented scale. As cars gradually become part of the Internet of Things (IoT) ecosystem, several stakeholders discover the value of in-vehicle network logs containing the measurements of the multitude of sensors deployed within the car. This wealth of data is also expected t…
CPCMs integrate causal drivers for robust portfolio optimization.
problem Degradation of classical portfolio models under structural breaks and lack of arbitrage consistency in machine learning.
method Causal PDE-Control Models integrating structural causal drivers, nonlinear filtering, and forward-backward PDE control.
result CPCM solvers achieve higher Sharpe ratios and lower turnover than benchmarks.
Optimizes portfolios using neural network approximations of asset sensitivities to common drivers.
problem Optimizing portfolios with complex asset dynamics and common drivers.
method Model asset dynamics with PDEs, approximate sensitivities with neural networks, and use hierarchical clustering on sensitivity matrix for optimization.
result Achieves over-performance in portfolio optimization across various markets and datasets.
We formalize causal separation in portfolio theory, deriving a closed-form projected Markowitz solution.
problem Portfolio optimization under causal separation conditions.
method Derive a closed-form solution for portfolio optimization using causal separation conditions.
result A closed-form projected Markowitz solution is derived under causal separation conditions.
TNDE quantifies dynamic gene drivers from single-cell snapshots.
problem Reconstructing time-resolved regulatory effects in biological processes.
method Time-varying Network Driver Estimation (TNDE) using shared graph attention encoder and partial optimal transport.
result TNDE identifies stage-specific driver genes in mouse erythropoiesis.
Order dispatching and driver repositioning (also known as fleet management) in the face of spatially and temporally varying supply and demand are central to a ride-sharing platform marketplace. Hand-crafting heuristic solutions that account for the dynamics in these resource allocation problems is difficult, and may be…
In this work, we propose a method for learning driver models that account for variables that cannot be observed directly. When trained on a synthetic dataset, our models are able to learn encodings for vehicle trajectories that distinguish between four distinct classes of driver behavior. Such encodings are learned wit…
Paper proposes personalized climate control for driver comfort.
problem Limited research on in-vehicle climate control and driver preferences.
method IoT platform for data collection, machine learning for driver behavior recognition, and personalized preference recommendation.
result Prototype demonstrates effective and accurate climate control for driver comfort.
Driver identification has emerged as a vital research field, where both practitioners and researchers investigate the potential of driver identification to enable a personalized driving experience. Within recent years, a selection of studies have reported that individuals could be perfectly identified based on their dr…
Study uses LCRN to detect driver distraction from EEG signals.
problem Improving road safety by detecting driver distraction.
method Used a Long-term Recurrent Convolutional Network (LCRN) for EEG-based driver distraction detection.
result LCRN model outperformed state-of-the-art TSC models in detecting driver distraction.
Paper tackles drowsy driving by learning from weakly labeled car acceleration data.
problem Lack of labeled data for estimating driver drowsiness.
method Weakly supervised learning, scalable stochastic optimization.
result Algorithm learns from weakly labeled data, outperforming baseline methods.
A large portion of passenger requests is reportedly unserviced, partially due to vacant for-hire drivers' cruising behavior during the passenger seeking process. This paper aims to model the multi-driver repositioning task through a mean field multi-agent reinforcement learning (MARL) approach that captures competition…
As automotive electronics continue to advance, cars are becoming more and more reliant on sensors to perform everyday driving operations. These sensors are omnipresent and help the car navigate, reduce accidents, and provide comfortable rides. However, they can also be used to learn about the drivers themselves. In thi…
Affective states have a critical role in driving performance and safety. They can degrade driver situation awareness and negatively impact cognitive processes, severely diminishing road safety. Therefore, detecting and assessing drivers' affective states is crucial in order to help improve the driving experience, and i…
Understanding and modeling human driver behavior is crucial for advanced vehicle development. However, unique driving styles, inconsistent behavior, and complex decision processes render it a challenging task, and existing approaches often lack variability or robustness. To approach this problem, we propose Probabilist…
Urban traffic systems worldwide are suffering from severe traffic safety problems. Traffic safety is affected by many complex factors, and heavily related to all drivers' behaviors involved in traffic system. Drivers with aggressive driving behaviors increase the risk of traffic accidents. In order to manage the safety…
Through deep learning and computer vision techniques, driving manoeuvres can be predicted accurately a few seconds in advance. Even though adapting a learned model to new drivers and different vehicles is key for robust driver-assistance systems, this problem has received little attention so far. This work proposes to …
Geometric BSDEsmath.PR
Develops geometric BSDEs for modeling dynamic return risk measures.
problem Modeling continuous-time dynamic return risk measures.
method Introduces and develops Geometric Backward Stochastic Differential Equations (GBSDEs) and two-driver BSDEs.
result Establishes existence, regularity, uniqueness, and stability of solutions to GBSDEs.
Study dynamic portfolio choice under rotating drivers, revealing a new geometric structure.
problem Investment under changing drivers with mutual independence.
method Analyzes geometric structure of portfolio choice, focusing on drivers and their rotation.
result Optimal policy separates into static and hedging components, reflecting the dynamic nature of drivers.
Bitcoin's price direction is better predicted without additional drivers during high volatility.
problem Predicting Bitcoin's price direction using various determinants.
method Continuous local transfer entropy for feature selection and deep learning classification model.
result Bitcoin's price direction can be better predicted without additional drivers during high volatility.
Study on price formation among investors with exponential utility and liabilities.
problem Equilibrium price formation among investors with heterogeneous risk-averseness and liabilities.
method Mean-field game theory and mean-field backward stochastic differential equations (BSDE).
result Existence of equilibrium risk-premium process and market clearing in the large population limit.
Modeling driver trajectories using inverse reinforcement learning and random utility.
problem Modeling rational driver behavior in road networks from sparse sensor data.
method Apply random utility theory to model unknown reward function, introduce extended state, and use Markov decision process.
result Maximum entropy inverse reinforcement learning is a special case of the proposed approach.
AI helps Vancouver identify where off-street parking saves time and space.
problem On-street parking inefficiencies and associated costs in Vancouver.
method Developed AI models for on-street and off-street parking, comparing time costs.
result Many areas off-street parking saves time and space, aligning with city goals.
We decompose the squared price-of-risk premium into three components: intervention-stable premium, confounding wedge, and information loss.
problem Decomposing the squared price-of-risk premium into its components
method Identifying an order-three obstruction to aggregation across portfolios
result The decomposition is estimable and detectable with a permutation-calibrated screen
Identifying the atmospheric drivers of drought and heat using a smoothed deep learning approachcs.LG
New model identifies anticyclonic patterns causing drought and heat.
problem Identifying atmospheric drivers of drought and heat.
method Smoothed convolutional neural network classifier for anticyclonic circulations.
result Helps identify important drivers of hot and dry extremes in climate simulations.
New formula for portfolio risk management using conditional PDEs.
problem Optimal diversification and risk management of portfolios.
method Closed-form formula for conditional probability, Gaussian copulas, conditional risk-neutral PDE.
result Dynamic monitoring of portfolio volatilities and weights from PDEs.
The World Health Organization (WHO) reported 1.25 million deaths yearly due to road traffic accidents worldwide and the number has been continuously increasing over the last few years. Nearly fifth of these accidents are caused by distracted drivers. Existing work of distracted driver detection is concerned with a smal…
New method for insurance valuation combining hedging and risk minimization.
problem Current insurance valuation methods do not reflect regulatory risk measures.
method Two-step hedging procedure using generalised regression.
result The method produces portfolios neutral to risk measures like VaR or expectiles.
This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated …
New machine learning model identifies key drivers of market troughs.
problem Misrepresentation of market trough drivers by simpler models.
method Flexible DML average partial effect causal machine learning framework.
result Volatility of options-implied risk appetite and market liquidity are key drivers.
Improved risk assessment for UBI using telematics data and AdaBoost.
problem Class imbalance in predicting claims frequency for UBI.
method Cost-sensitive multi-class AdaBoost (SAMME.C2) algorithm.
result SAMME.C2 outperforms other models in handling class imbalances.
A Rapid Pattern-Recognition Method for Driving Types Using Clustering-Based Support Vector Machinesstat.ML
A rapid pattern-recognition approach to characterize driver's curve-negotiating behavior is proposed. To shorten the recognition time and improve the recognition of driving styles, a k-means clustering-based support vector machine ( kMC-SVM) method is developed and used for classifying drivers into two types: aggressiv…
Study on BSDEs with random time horizon, focusing on existence and properties.
problem Existence of solutions to BSDEs and reflected BSDEs with a random time horizon.
method Method of reduction and examination of BSDEs with lahdlaug driver.
result Existence of solutions to BSDEs and reflected BSDEs with a random time horizon.
This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is formulated as a continuous time stochastic optimal control problem aiming at ma…