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arXiv research

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.

169,291 papers · 148 categories

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6 results for Black-Scholes-Barenblatt

Study Asian option pricing under uncertain volatility, approximating prices with small volatility intervals.

problem Asian option pricing in uncertain volatility conditions.
method Procedure to approximate Asian option prices with small volatility intervals, solving fully nonlinear PDE.
result Approximation method for solving fully nonlinear PDE.

The paper derives upper hedging prices for multivariate contingent claims using game-theoretic probability and submodularity.

problem Deriving upper hedging prices for complex financial contracts.
method Game-theoretic approach, optimization over simplexes, Lovász extension, Black-Scholes-Barenblatt equations.
result Upper and lower hedging prices can be calculated efficiently for submodular or supermodular payoff functions.

Deep neural networks solve high-dimensional PDEs without explicit grids.

problem Solving high-dimensional PDEs using classical methods is computationally infeasible.
method Approximate solution with a deep neural network trained via FBSDEs.
result Deep learning can solve high-dimensional PDEs efficiently.

Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets and option markets with uncertain prior distribution are established by Peng's G-s…

2014-07-30abs ↗pdf ↗

New method solves high-dimensional PDEs and 2BSDEs efficiently.

problem High-dimensional fully nonlinear PDEs and 2BSDEs in financial models.
method Connection between PDEs and 2BSDEs, merged formulation, temporal discretization, spatial approximation via neural nets, stochastic gradient descent.
result Efficient and accurate solution for high-dimensional nonlinear expectations.