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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.

169,181 papers · 148 categories

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5 results for “sub-martingales”

Generalization of Doob's Inequality and A Tighter Estimate on Look-back Option Priceq-fin.MF

Enhances Doob's inequality for sub-martingales.

problem Fundamental importance of Doob's inequality in stochastic process theory.

method Generalization of Doob's

L^p

inequality for sub-martingales.

result A tighter estimate on Doob's inequality for sub-martingales.

Doob's inequality sub-martingales stochastic processes

2018-07-06abs ↗pdf ↗

Reflected BSDE with a Constraint and a New Doob-Meyer Nonlinear Decompositionmath.PR

In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. We then apply the results to the pricing of American o…

2006-11-28abs ↗pdf ↗

Risk Premium Impact in the Perturbative Black Scholes Modelq-fin.PR

We study the risk premium impact in the Perturbative Black Scholes model. The Perturbative Black Scholes model, developed by Scotti, is a subjective volatility model based on the classical Black Scholes one, where the volatility used by the trader is an estimation of the market one and contains measurement errors. In t…

2008-06-02abs ↗pdf ↗

Time consistency of dynamic risk measures and dynamic performance measures generated by distortion functionsq-fin.RM

Study dynamic risk measures and performance indices using distortion functions.

problem Investigate time consistency of dynamic risk measures and performance indices generated by distortion functions.

method Analyze dynamic coherent risk measures (DCRMs) and dynamic weighted value at risk measures, proving their equivalence. Establish properties of families of DCRMs generated by distortion functions and define corresponding dynamic coherent acceptability indices (DCAIs). Examine time consistency of DCRMs and DCAIs.

result DCRM generated by distortion functions are sub-martingale time consistent but not super-martingale time consistent and not weakly acceptance time consistent.

distortion functions dynamic risk measures dynamic performance measures time consistency coherent acceptability indices

2023-09-05abs ↗pdf ↗

Trading under the Proof-of-Stake Protocol -- a Continuous-Time Control Approachecon.GN

Optimal trading strategy in Proof-of-Stake blockchain using continuous-time control.

problem Finding the optimal balance between stake utility and consumption utility in Proof-of-Stake blockchain.

method Continuous-time control approach, dynamic programming, Hamilton-Jacobi-Bellman (HJB) equations.

result Close-form solutions for linear and convex utility functions, optimal strategies identified.

Proof-of-Stake Blockchain Optimal Trading Continuous-Time Control Dynamic Programming

2022-07-26abs ↗pdf ↗