Transition Probability of Brownian Motion in the Octant and its Application to Default Modelling

DOI10.1080/1350486X.2018.1481439zbMath1411.91601arXiv1801.00362OpenAlexW2963296441MaRDI QIDQ5742504

Vadim Kaushansky, Alexander Lipton-Lifschitz, Christoph Reisinger

Publication date: 15 May 2019

Published in: Applied Mathematical Finance (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.00362

zbMATH Keywords

nonlinear eigenvalue problemtransition probabilitythree-dimensional Brownian motionstructural default modelmutual liabilities

Mathematics Subject Classification ID

Financial applications of other theories (91G80) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Credit risk (91G40) Software, source code, etc. for problems pertaining to game theory, economics, and finance (91-04)

Related Items (4)

Simulation of reflected Brownian motion on two dimensional wedges ⋮ Dynamic contagion in a banking system with births and defaults ⋮ On the first hitting time density for a reducible diffusion process ⋮ Semi-analytical solution of a McKean–Vlasov equation with feedback through hitting a boundary

Uses Software

• Chebfun
• rootsb

Cites Work

• An integral method for solving nonlinear eigenvalue problems
• Structural default model with mutual obligations
• Fast linear algebra is stable
• Computing the common zeros of two bivariate functions via Bézout resultants
• Double Lookbacks
• Efficient solution of structural default models with correlated jumps and mutual obligations
• MODERN MONETARY CIRCUIT THEORY, STABILITY OF INTERCONNECTED BANKING NETWORK, AND BALANCE SHEET OPTIMIZATION FOR INDIVIDUAL BANKS
• Pricing credit default swaps with bilateral value adjustments
• Systemic Risk in Financial Systems
• Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
• A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions
• Three dimensional distribution of Brownian motion extrema
• The impact of a natural time change on the convergence of the Crank-Nicolson scheme
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