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This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering

Research & information: general --- Mathematics & science --- delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation --- delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation

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"Credit risk is today one of the most intensely studied topics in quantitative finance. This book provides an introduction and overview for readers who seek an up-to-date reference to the central problems of the field and to the tools currently used to analyze them. The book is aimed at researchers and students in finance, at quantitative analysts in banks and other financial institutions, and at regulators interested in the modeling aspects of credit risk."--Jacket.

Credit --- Management. --- Adapted process. --- Arbitrage. --- Asset Sales. --- Asset. --- Bankruptcy. --- Barrier option. --- Basis Point. --- Binomial approximation. --- Binomial distribution. --- Bond (finance). --- Bond Yield. --- Bond valuation. --- Calculation. --- Call option. --- Capital structure. --- Comparative advantage. --- Convenience yield. --- Coupon (bond). --- Coupon. --- Credit (finance). --- Credit default swap. --- Credit derivative. --- Credit rating. --- Credit risk. --- Credit spread (options). --- Cumulative Dividend. --- Current liability. --- Debt Issue. --- Debt. --- Discount function. --- Discrete time and continuous time. --- Dividend payout ratio. --- Dividend. --- Equity value. --- Equivalent Martingale Measures. --- Estimation. --- Estimator. --- Exponential distribution. --- Fair value. --- Geometric Brownian motion. --- Government bond. --- High-yield debt. --- Implicit cost. --- Implied volatility. --- Information asymmetry. --- Interest rate swap. --- Interest rate. --- Issuer. --- Jump process. --- Latent variable. --- Least squares. --- Leverage (finance). --- Liability (financial accounting). --- Libor. --- Logistic regression. --- Market liquidity. --- Market value. --- Markov chain. --- Markov model. --- Mathematical finance. --- Merton Model. --- Moment-generating function. --- Money market. --- Option (finance). --- Par Yield Curve. --- Path dependence. --- Payment. --- Plain vanilla. --- Predictable process. --- Present value. --- Pricing. --- Probability of default. --- Probability. --- Put option. --- Random variable. --- Recapitalization. --- Repurchase agreement. --- Risk management. --- Risk premium. --- Risk-neutral measure. --- Semimartingale. --- Short rate. --- State variable. --- Swap (finance). --- Swap Curve. --- Swap rate. --- Swap spread. --- Synthetic CDO. --- Tax advantage. --- Tax shield. --- Tax. --- Trading strategy. --- Tranche. --- Underlying Security. --- Value (economics). --- Variance. --- Vasicek model. --- Yield curve. --- Yield spread. --- Zero-coupon bond.